%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA014+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:37 AM UTC 2025
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRA014+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 15:23:39 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(green_type, type, (
% 0.14/0.41 green: ( $i * $i ) > $o)).
% 0.14/0.41 tff(n5_type, type, (
% 0.14/0.41 n5: $i)).
% 0.14/0.41 tff(n1_type, type, (
% 0.14/0.41 n1: $i)).
% 0.14/0.41 tff(red_type, type, (
% 0.14/0.41 red: ( $i * $i ) > $o)).
% 0.14/0.41 tff(n6_type, type, (
% 0.14/0.41 n6: $i)).
% 0.14/0.41 tff(n3_type, type, (
% 0.14/0.41 n3: $i)).
% 0.14/0.41 tff(n2_type, type, (
% 0.14/0.41 n2: $i)).
% 0.14/0.41 tff(n4_type, type, (
% 0.14/0.41 n4: $i)).
% 0.14/0.41 tff(goal_type, type, (
% 0.14/0.41 goal: $o)).
% 0.14/0.41 tff(less_than_type, type, (
% 0.14/0.41 less_than: ( $i * $i ) > $o)).
% 0.14/0.41 tff(1,assumption,(green(n5, n6)), introduced(assumption)).
% 0.14/0.41 tff(2,assumption,(red(n3, n5)), introduced(assumption)).
% 0.14/0.41 tff(3,assumption,(green(n2, n5)), introduced(assumption)).
% 0.14/0.41 tff(4,assumption,(green(n2, n4)), introduced(assumption)).
% 0.14/0.41 tff(5,assumption,(red(n4, n5)), introduced(assumption)).
% 0.14/0.41 tff(6,assumption,(red(n2, n6)), introduced(assumption)).
% 0.14/0.41 tff(7,assumption,(green(n1, n6)), introduced(assumption)).
% 0.14/0.41 tff(8,assumption,(green(n1, n5)), introduced(assumption)).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 ((~goal) <=> (~goal)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(10,axiom,(~goal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goal_to_be_proved')).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (~goal),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : refl((goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C))) <=> (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C))) <=> ![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((green(A, B) & green(B, C) & green(A, C)) <=> (~((~green(A, B)) | (~green(B, C)) | (~green(A, C))))), ((~(green(A, B) & green(B, C) & green(A, C))) <=> (~(~((~green(A, B)) | (~green(B, C)) | (~green(A, C))))))), rewrite((~(~((~green(A, B)) | (~green(B, C)) | (~green(A, C))))) <=> ((~green(A, B)) | (~green(B, C)) | (~green(A, C)))), ((~(green(A, B) & green(B, C) & green(A, C))) <=> ((~green(A, B)) | (~green(B, C)) | (~green(A, C))))), ((goal | (~(green(A, B) & green(B, C) & green(A, C)))) <=> (goal | ((~green(A, B)) | (~green(B, C)) | (~green(A, C)))))), rewrite((goal | ((~green(A, B)) | (~green(B, C)) | (~green(A, C)))) <=> (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))), ((goal | (~(green(A, B) & green(B, C) & green(A, C)))) <=> (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (goal | (~(green(A, B) & green(B, C) & green(A, C)))) <=> ![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (goal | (~(green(A, B) & green(B, C) & green(A, C)))) <=> ![A: $i, B: $i, C: $i] : (goal | (~(green(A, B) & green(B, C) & green(A, C))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((green(A, B) & green(B, C)) & green(A, C)) <=> (green(A, B) & green(B, C) & green(A, C))), ((((green(A, B) & green(B, C)) & green(A, C)) => goal) <=> ((green(A, B) & green(B, C) & green(A, C)) => goal))), rewrite(((green(A, B) & green(B, C) & green(A, C)) => goal) <=> (goal | (~(green(A, B) & green(B, C) & green(A, C))))), ((((green(A, B) & green(B, C)) & green(A, C)) => goal) <=> (goal | (~(green(A, B) & green(B, C) & green(A, C))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (((green(A, B) & green(B, C)) & green(A, C)) => goal) <=> ![A: $i, B: $i, C: $i] : (goal | (~(green(A, B) & green(B, C) & green(A, C))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.41 tff(19,axiom,(![A: $i, B: $i, C: $i] : (((green(A, B) & green(B, C)) & green(A, C)) => goal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','green_clique')).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (goal | (~(green(A, B) & green(B, C) & green(A, C))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (goal | (~(green(A, B) & green(B, C) & green(A, C))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.14/0.41 tff(22,plain,(
% 0.14/0.41 ![A: $i, B: $i, C: $i] : (goal | (~(green(A, B) & green(B, C) & green(A, C))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[21])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n6)) | (~green(n1, n5)) | (~green(n5, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n6)) | (~green(n1, n5)) | (~green(n5, n6)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 ((goal | (~green(n1, n5)) | (~green(n5, n6)) | (~green(n1, n6))) <=> (goal | (~green(n1, n6)) | (~green(n1, n5)) | (~green(n5, n6)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n5)) | (~green(n5, n6)) | (~green(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n6)) | (~green(n1, n5)) | (~green(n5, n6))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[26])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n5)) | (~green(n5, n6)) | (~green(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n6)) | (~green(n1, n5)) | (~green(n5, n6)))),
% 0.14/0.41 inference(transitivity,[status(thm)],[27, 25])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n5)) | (~green(n5, n6)) | (~green(n1, n6)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n6)) | (~green(n1, n5)) | (~green(n5, n6))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[30, 24, 11, 1, 8, 7])).
% 0.14/0.41 tff(32,plain,((~green(n1, n5)) | (~green(n5, n6)) | (~green(n1, n6))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (~green(n1, n5)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[32, 7, 1])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B))) <=> ![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((less_than(A, B) & less_than(B, C)) <=> (~((~less_than(B, C)) | (~less_than(A, B))))), ((~(less_than(A, B) & less_than(B, C))) <=> (~(~((~less_than(B, C)) | (~less_than(A, B))))))), rewrite((~(~((~less_than(B, C)) | (~less_than(A, B))))) <=> ((~less_than(B, C)) | (~less_than(A, B)))), ((~(less_than(A, B) & less_than(B, C))) <=> ((~less_than(B, C)) | (~less_than(A, B))))), (((~(less_than(A, B) & less_than(B, C))) | less_than(A, C)) <=> (((~less_than(B, C)) | (~less_than(A, B))) | less_than(A, C)))), rewrite((((~less_than(B, C)) | (~less_than(A, B))) | less_than(A, C)) <=> (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))), (((~(less_than(A, B) & less_than(B, C))) | less_than(A, C)) <=> (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~(less_than(A, B) & less_than(B, C))) | less_than(A, C)) <=> ![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~(less_than(A, B) & less_than(B, C))) | less_than(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(less_than(A, B) & less_than(B, C))) | less_than(A, C))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((less_than(A, B) & less_than(B, C)) => less_than(A, C)) <=> ((~(less_than(A, B) & less_than(B, C))) | less_than(A, C)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((less_than(A, B) & less_than(B, C)) => less_than(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(less_than(A, B) & less_than(B, C))) | less_than(A, C))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.41 tff(40,axiom,(![A: $i, B: $i, C: $i] : ((less_than(A, B) & less_than(B, C)) => less_than(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less_than_transitive')).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~(less_than(A, B) & less_than(B, C))) | less_than(A, C))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.14/0.41 tff(42,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : ((~(less_than(A, B) & less_than(B, C))) | less_than(A, C))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.14/0.41 tff(43,plain,(
% 0.14/0.41 ![A: $i, B: $i, C: $i] : ((~(less_than(A, B) & less_than(B, C))) | less_than(A, C))),
% 0.14/0.41 inference(skolemize,[status(sab)],[42])).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 (![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (less_than(n4, n5) <=> less_than(n4, n5)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(47,axiom,((((less_than(n1, n2) & less_than(n2, n3)) & less_than(n3, n4)) & less_than(n4, n5)) & less_than(n5, n6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ordering')).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 (((less_than(n1, n2) & less_than(n2, n3)) & less_than(n3, n4)) & less_than(n4, n5)),
% 0.14/0.41 inference(and_elim,[status(thm)],[47])).
% 0.14/0.41 tff(49,plain,
% 0.14/0.41 (less_than(n4, n5)),
% 0.14/0.41 inference(and_elim,[status(thm)],[48])).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 (less_than(n4, n5)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 (less_than(n3, n4) <=> less_than(n3, n4)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 ((less_than(n1, n2) & less_than(n2, n3)) & less_than(n3, n4)),
% 0.14/0.41 inference(and_elim,[status(thm)],[48])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 (less_than(n3, n4)),
% 0.14/0.41 inference(and_elim,[status(thm)],[52])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 (less_than(n3, n4)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[53, 51])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n3, n4)) | less_than(n3, n5) | (~less_than(n4, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n3, n4)) | less_than(n3, n5) | (~less_than(n4, n5)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 ((less_than(n3, n5) | (~less_than(n4, n5)) | (~less_than(n3, n4))) <=> ((~less_than(n3, n4)) | less_than(n3, n5) | (~less_than(n4, n5)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n3, n5) | (~less_than(n4, n5)) | (~less_than(n3, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n3, n4)) | less_than(n3, n5) | (~less_than(n4, n5))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n3, n5) | (~less_than(n4, n5)) | (~less_than(n3, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n3, n4)) | less_than(n3, n5) | (~less_than(n4, n5)))),
% 0.14/0.41 inference(transitivity,[status(thm)],[57, 55])).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n3, n5) | (~less_than(n4, n5)) | (~less_than(n3, n4)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(60,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n3, n4)) | less_than(n3, n5) | (~less_than(n4, n5))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.14/0.41 tff(61,plain,
% 0.14/0.41 (less_than(n3, n5)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[60, 54, 50, 45])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 (less_than(n2, n3) <=> less_than(n2, n3)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 (less_than(n1, n2) & less_than(n2, n3)),
% 0.14/0.41 inference(and_elim,[status(thm)],[52])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 (less_than(n2, n3)),
% 0.14/0.41 inference(and_elim,[status(thm)],[63])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 (less_than(n2, n3)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[64, 62])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 (less_than(n1, n2) <=> less_than(n1, n2)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 (less_than(n1, n2)),
% 0.14/0.41 inference(and_elim,[status(thm)],[63])).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 (less_than(n1, n2)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.14/0.41 tff(69,plain,
% 0.14/0.41 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n3) | (~less_than(n2, n3)) | (~less_than(n1, n2)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | less_than(n1, n3) | (~less_than(n2, n3)) | (~less_than(n1, n2)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n3) | (~less_than(n2, n3)) | (~less_than(n1, n2)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | less_than(n1, n3) | (~less_than(n2, n3)) | (~less_than(n1, n2))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 (less_than(n1, n3)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[71, 68, 65, 45])).
% 0.14/0.42 tff(73,plain,
% 0.14/0.42 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n1, n3)) | less_than(n1, n5) | (~less_than(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n1, n3)) | less_than(n1, n5) | (~less_than(n3, n5)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(74,plain,
% 0.14/0.42 ((less_than(n1, n5) | (~less_than(n3, n5)) | (~less_than(n1, n3))) <=> ((~less_than(n1, n3)) | less_than(n1, n5) | (~less_than(n3, n5)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(75,plain,
% 0.14/0.42 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n5) | (~less_than(n3, n5)) | (~less_than(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n1, n3)) | less_than(n1, n5) | (~less_than(n3, n5))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.14/0.42 tff(76,plain,
% 0.14/0.42 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n5) | (~less_than(n3, n5)) | (~less_than(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n1, n3)) | less_than(n1, n5) | (~less_than(n3, n5)))),
% 0.14/0.42 inference(transitivity,[status(thm)],[75, 73])).
% 0.14/0.42 tff(77,plain,
% 0.14/0.42 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n5) | (~less_than(n3, n5)) | (~less_than(n1, n3)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(78,plain,
% 0.14/0.42 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n1, n3)) | less_than(n1, n5) | (~less_than(n3, n5))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.14/0.42 tff(79,plain,
% 0.14/0.42 (less_than(n1, n5)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[78, 45, 72, 61])).
% 0.14/0.42 tff(80,plain,
% 0.14/0.42 (^[A: $i, B: $i] : refl((red(A, B) | green(A, B) | (~less_than(A, B))) <=> (red(A, B) | green(A, B) | (~less_than(A, B))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(81,plain,
% 0.22/0.42 (![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B))) <=> ![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.22/0.42 tff(82,plain,
% 0.22/0.42 (![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B))) <=> ![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(83,plain,
% 0.22/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite((red(A, B) | green(A, B)) <=> (red(A, B) | green(A, B))), ((less_than(A, B) => (red(A, B) | green(A, B))) <=> (less_than(A, B) => (red(A, B) | green(A, B))))), rewrite((less_than(A, B) => (red(A, B) | green(A, B))) <=> (red(A, B) | green(A, B) | (~less_than(A, B)))), ((less_than(A, B) => (red(A, B) | green(A, B))) <=> (red(A, B) | green(A, B) | (~less_than(A, B)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(84,plain,
% 0.22/0.42 (![A: $i, B: $i] : (less_than(A, B) => (red(A, B) | green(A, B))) <=> ![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.22/0.42 tff(85,axiom,(![A: $i, B: $i] : (less_than(A, B) => (red(A, B) | green(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','partition')).
% 0.22/0.42 tff(86,plain,
% 0.22/0.42 (![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.22/0.42 tff(87,plain,
% 0.22/0.42 (![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.22/0.42 tff(88,plain,(
% 0.22/0.42 ![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[87])).
% 0.22/0.42 tff(89,plain,
% 0.22/0.42 (![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.22/0.42 tff(90,plain,
% 0.22/0.42 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n5) | green(n1, n5) | (~less_than(n1, n5)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n1, n5) | green(n1, n5) | (~less_than(n1, n5)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(91,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n5) | green(n1, n5) | (~less_than(n1, n5)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(92,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n1, n5) | green(n1, n5) | (~less_than(n1, n5))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.22/0.42 tff(93,plain,
% 0.22/0.42 (red(n1, n5) | green(n1, n5)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.22/0.42 tff(94,plain,
% 0.22/0.42 (red(n1, n5)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[93, 33])).
% 0.22/0.42 tff(95,assumption,(red(n1, n5)), introduced(assumption)).
% 0.22/0.42 tff(96,assumption,(red(n1, n4)), introduced(assumption)).
% 0.22/0.42 tff(97,plain,
% 0.22/0.42 (^[A: $i, B: $i, C: $i] : refl((goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C))) <=> (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(98,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C))) <=> ![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.22/0.42 tff(99,plain,
% 0.22/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((red(A, B) & red(B, C) & red(A, C)) <=> (~((~red(A, B)) | (~red(B, C)) | (~red(A, C))))), ((~(red(A, B) & red(B, C) & red(A, C))) <=> (~(~((~red(A, B)) | (~red(B, C)) | (~red(A, C))))))), rewrite((~(~((~red(A, B)) | (~red(B, C)) | (~red(A, C))))) <=> ((~red(A, B)) | (~red(B, C)) | (~red(A, C)))), ((~(red(A, B) & red(B, C) & red(A, C))) <=> ((~red(A, B)) | (~red(B, C)) | (~red(A, C))))), ((goal | (~(red(A, B) & red(B, C) & red(A, C)))) <=> (goal | ((~red(A, B)) | (~red(B, C)) | (~red(A, C)))))), rewrite((goal | ((~red(A, B)) | (~red(B, C)) | (~red(A, C)))) <=> (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))), ((goal | (~(red(A, B) & red(B, C) & red(A, C)))) <=> (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(100,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (goal | (~(red(A, B) & red(B, C) & red(A, C)))) <=> ![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.22/0.42 tff(101,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (goal | (~(red(A, B) & red(B, C) & red(A, C)))) <=> ![A: $i, B: $i, C: $i] : (goal | (~(red(A, B) & red(B, C) & red(A, C))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(102,plain,
% 0.22/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((red(A, B) & red(B, C)) & red(A, C)) <=> (red(A, B) & red(B, C) & red(A, C))), ((((red(A, B) & red(B, C)) & red(A, C)) => goal) <=> ((red(A, B) & red(B, C) & red(A, C)) => goal))), rewrite(((red(A, B) & red(B, C) & red(A, C)) => goal) <=> (goal | (~(red(A, B) & red(B, C) & red(A, C))))), ((((red(A, B) & red(B, C)) & red(A, C)) => goal) <=> (goal | (~(red(A, B) & red(B, C) & red(A, C))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(103,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (((red(A, B) & red(B, C)) & red(A, C)) => goal) <=> ![A: $i, B: $i, C: $i] : (goal | (~(red(A, B) & red(B, C) & red(A, C))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[102])).
% 0.22/0.42 tff(104,axiom,(![A: $i, B: $i, C: $i] : (((red(A, B) & red(B, C)) & red(A, C)) => goal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','red_clique')).
% 0.22/0.42 tff(105,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (goal | (~(red(A, B) & red(B, C) & red(A, C))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.22/0.42 tff(106,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (goal | (~(red(A, B) & red(B, C) & red(A, C))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.22/0.42 tff(107,plain,(
% 0.22/0.42 ![A: $i, B: $i, C: $i] : (goal | (~(red(A, B) & red(B, C) & red(A, C))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[106])).
% 0.22/0.42 tff(108,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.22/0.42 tff(109,plain,
% 0.22/0.42 (![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.22/0.42 tff(110,plain,
% 0.22/0.42 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n4)) | (~red(n4, n5)) | (~red(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n4)) | (~red(n4, n5)) | (~red(n1, n5)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(111,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n4)) | (~red(n4, n5)) | (~red(n1, n5)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(112,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n4)) | (~red(n4, n5)) | (~red(n1, n5))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.42 tff(113,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[112, 109, 11, 5, 96, 95])).
% 0.22/0.42 tff(114,plain,((~red(n1, n4)) | (~red(n4, n5)) | (~red(n1, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(115,plain,
% 0.22/0.42 (~red(n1, n4)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[114, 94, 5])).
% 0.22/0.42 tff(116,plain,
% 0.22/0.42 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n3, n4)) | (~less_than(n1, n3)) | less_than(n1, n4))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n3, n4)) | (~less_than(n1, n3)) | less_than(n1, n4))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(117,plain,
% 0.22/0.42 ((less_than(n1, n4) | (~less_than(n3, n4)) | (~less_than(n1, n3))) <=> ((~less_than(n3, n4)) | (~less_than(n1, n3)) | less_than(n1, n4))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(118,plain,
% 0.22/0.42 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n4) | (~less_than(n3, n4)) | (~less_than(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n3, n4)) | (~less_than(n1, n3)) | less_than(n1, n4)))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.22/0.42 tff(119,plain,
% 0.22/0.42 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n4) | (~less_than(n3, n4)) | (~less_than(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n3, n4)) | (~less_than(n1, n3)) | less_than(n1, n4))),
% 0.22/0.42 inference(transitivity,[status(thm)],[118, 116])).
% 0.22/0.42 tff(120,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n4) | (~less_than(n3, n4)) | (~less_than(n1, n3)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(121,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n3, n4)) | (~less_than(n1, n3)) | less_than(n1, n4)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.22/0.42 tff(122,plain,
% 0.22/0.42 (less_than(n1, n4)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[121, 54, 45, 72])).
% 0.22/0.42 tff(123,plain,
% 0.22/0.42 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n4) | green(n1, n4) | (~less_than(n1, n4)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n1, n4) | green(n1, n4) | (~less_than(n1, n4)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(124,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n4) | green(n1, n4) | (~less_than(n1, n4)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(125,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n1, n4) | green(n1, n4) | (~less_than(n1, n4))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.22/0.42 tff(126,plain,
% 0.22/0.42 (red(n1, n4) | green(n1, n4)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[125, 89, 122])).
% 0.22/0.42 tff(127,plain,
% 0.22/0.42 (green(n1, n4)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[126, 115])).
% 0.22/0.42 tff(128,assumption,(green(n1, n4)), introduced(assumption)).
% 0.22/0.42 tff(129,assumption,(green(n4, n6)), introduced(assumption)).
% 0.22/0.42 tff(130,plain,
% 0.22/0.42 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n4, n6)) | (~green(n1, n4)) | (~green(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n4, n6)) | (~green(n1, n4)) | (~green(n1, n6)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(131,plain,
% 0.22/0.42 ((goal | (~green(n1, n4)) | (~green(n4, n6)) | (~green(n1, n6))) <=> (goal | (~green(n4, n6)) | (~green(n1, n4)) | (~green(n1, n6)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(132,plain,
% 0.22/0.42 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n4, n6)) | (~green(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n4, n6)) | (~green(n1, n4)) | (~green(n1, n6))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[131])).
% 0.22/0.42 tff(133,plain,
% 0.22/0.42 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n4, n6)) | (~green(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n4, n6)) | (~green(n1, n4)) | (~green(n1, n6)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[132, 130])).
% 0.22/0.42 tff(134,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n4, n6)) | (~green(n1, n6)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(135,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n4, n6)) | (~green(n1, n4)) | (~green(n1, n6))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.22/0.42 tff(136,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[135, 24, 11, 129, 128, 7])).
% 0.22/0.42 tff(137,plain,((~green(n4, n6)) | (~green(n1, n4)) | (~green(n1, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(138,plain,
% 0.22/0.43 (~green(n4, n6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[137, 127, 7])).
% 0.22/0.43 tff(139,plain,
% 0.22/0.43 (less_than(n5, n6) <=> less_than(n5, n6)),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(140,plain,
% 0.22/0.43 (less_than(n5, n6)),
% 0.22/0.43 inference(and_elim,[status(thm)],[47])).
% 0.22/0.43 tff(141,plain,
% 0.22/0.43 (less_than(n5, n6)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.22/0.43 tff(142,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n4, n5)) | less_than(n4, n6) | (~less_than(n5, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n5)) | less_than(n4, n6) | (~less_than(n5, n6)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(143,plain,
% 0.22/0.43 ((less_than(n4, n6) | (~less_than(n5, n6)) | (~less_than(n4, n5))) <=> ((~less_than(n4, n5)) | less_than(n4, n6) | (~less_than(n5, n6)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(144,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n4, n6) | (~less_than(n5, n6)) | (~less_than(n4, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n4, n5)) | less_than(n4, n6) | (~less_than(n5, n6))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[143])).
% 0.22/0.43 tff(145,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n4, n6) | (~less_than(n5, n6)) | (~less_than(n4, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n5)) | less_than(n4, n6) | (~less_than(n5, n6)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[144, 142])).
% 0.22/0.43 tff(146,plain,
% 0.22/0.43 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n4, n6) | (~less_than(n5, n6)) | (~less_than(n4, n5)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(147,plain,
% 0.22/0.43 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n5)) | less_than(n4, n6) | (~less_than(n5, n6))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.22/0.43 tff(148,plain,
% 0.22/0.43 (less_than(n4, n6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[147, 50, 141, 45])).
% 0.22/0.43 tff(149,plain,
% 0.22/0.43 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n4, n6)) | red(n4, n6) | green(n4, n6))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n4, n6)) | red(n4, n6) | green(n4, n6))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(150,plain,
% 0.22/0.43 ((red(n4, n6) | green(n4, n6) | (~less_than(n4, n6))) <=> ((~less_than(n4, n6)) | red(n4, n6) | green(n4, n6))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(151,plain,
% 0.22/0.43 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n4, n6) | green(n4, n6) | (~less_than(n4, n6)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n4, n6)) | red(n4, n6) | green(n4, n6)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[150])).
% 0.22/0.43 tff(152,plain,
% 0.22/0.43 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n4, n6) | green(n4, n6) | (~less_than(n4, n6)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n4, n6)) | red(n4, n6) | green(n4, n6))),
% 0.22/0.43 inference(transitivity,[status(thm)],[151, 149])).
% 0.22/0.43 tff(153,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n4, n6) | green(n4, n6) | (~less_than(n4, n6)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(154,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n4, n6)) | red(n4, n6) | green(n4, n6)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.22/0.43 tff(155,plain,
% 0.22/0.43 (red(n4, n6) | green(n4, n6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[154, 89, 148])).
% 0.22/0.43 tff(156,plain,
% 0.22/0.43 (red(n4, n6)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[155, 138])).
% 0.22/0.43 tff(157,assumption,(red(n4, n6)), introduced(assumption)).
% 0.22/0.43 tff(158,assumption,(red(n2, n4)), introduced(assumption)).
% 0.22/0.43 tff(159,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n6)) | (~red(n4, n6)) | (~red(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n2, n6)) | (~red(n4, n6)) | (~red(n2, n4)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(160,plain,
% 0.22/0.43 ((goal | (~red(n2, n4)) | (~red(n4, n6)) | (~red(n2, n6))) <=> (goal | (~red(n2, n6)) | (~red(n4, n6)) | (~red(n2, n4)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(161,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n4)) | (~red(n4, n6)) | (~red(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n6)) | (~red(n4, n6)) | (~red(n2, n4))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[160])).
% 0.22/0.43 tff(162,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n4)) | (~red(n4, n6)) | (~red(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n2, n6)) | (~red(n4, n6)) | (~red(n2, n4)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[161, 159])).
% 0.22/0.43 tff(163,plain,
% 0.22/0.43 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n4)) | (~red(n4, n6)) | (~red(n2, n6)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(164,plain,
% 0.22/0.43 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n2, n6)) | (~red(n4, n6)) | (~red(n2, n4))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.22/0.43 tff(165,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[164, 109, 11, 158, 157, 6])).
% 0.22/0.43 tff(166,plain,((~red(n2, n4)) | (~red(n4, n6)) | (~red(n2, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(167,plain,
% 0.22/0.43 (~red(n2, n4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[166, 156, 6])).
% 0.22/0.43 tff(168,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n2, n3)) | less_than(n2, n4) | (~less_than(n3, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n2, n3)) | less_than(n2, n4) | (~less_than(n3, n4)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(169,plain,
% 0.22/0.43 ((less_than(n2, n4) | (~less_than(n3, n4)) | (~less_than(n2, n3))) <=> ((~less_than(n2, n3)) | less_than(n2, n4) | (~less_than(n3, n4)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(170,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n4) | (~less_than(n3, n4)) | (~less_than(n2, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n2, n3)) | less_than(n2, n4) | (~less_than(n3, n4))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[169])).
% 0.22/0.43 tff(171,plain,
% 0.22/0.43 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n4) | (~less_than(n3, n4)) | (~less_than(n2, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n2, n3)) | less_than(n2, n4) | (~less_than(n3, n4)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[170, 168])).
% 0.22/0.43 tff(172,plain,
% 0.22/0.43 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n4) | (~less_than(n3, n4)) | (~less_than(n2, n3)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(173,plain,
% 0.22/0.43 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n2, n3)) | less_than(n2, n4) | (~less_than(n3, n4))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.22/0.43 tff(174,plain,
% 0.22/0.43 (less_than(n2, n4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[173, 65, 54, 45])).
% 0.22/0.43 tff(175,plain,
% 0.22/0.43 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n4) | green(n2, n4) | (~less_than(n2, n4)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n2, n4) | green(n2, n4) | (~less_than(n2, n4)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(176,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n4) | green(n2, n4) | (~less_than(n2, n4)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(177,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n2, n4) | green(n2, n4) | (~less_than(n2, n4))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.22/0.44 tff(178,plain,
% 0.22/0.44 (red(n2, n4) | green(n2, n4)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[177, 89, 174])).
% 0.22/0.44 tff(179,plain,
% 0.22/0.44 (green(n2, n4)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[178, 167])).
% 0.22/0.44 tff(180,assumption,(red(n3, n4)), introduced(assumption)).
% 0.22/0.44 tff(181,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n4)) | (~red(n4, n6)) | (~red(n3, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n3, n4)) | (~red(n4, n6)) | (~red(n3, n6)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(182,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n4)) | (~red(n4, n6)) | (~red(n3, n6)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(183,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n3, n4)) | (~red(n4, n6)) | (~red(n3, n6))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.22/0.44 tff(184,plain,
% 0.22/0.44 (~red(n3, n6)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[183, 109, 11, 180, 157])).
% 0.22/0.44 tff(185,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n5, n6)) | (~less_than(n3, n5)) | less_than(n3, n6))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n5, n6)) | (~less_than(n3, n5)) | less_than(n3, n6))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(186,plain,
% 0.22/0.44 ((less_than(n3, n6) | (~less_than(n5, n6)) | (~less_than(n3, n5))) <=> ((~less_than(n5, n6)) | (~less_than(n3, n5)) | less_than(n3, n6))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(187,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n3, n6) | (~less_than(n5, n6)) | (~less_than(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n5, n6)) | (~less_than(n3, n5)) | less_than(n3, n6)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[186])).
% 0.22/0.44 tff(188,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n3, n6) | (~less_than(n5, n6)) | (~less_than(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n5, n6)) | (~less_than(n3, n5)) | less_than(n3, n6))),
% 0.22/0.44 inference(transitivity,[status(thm)],[187, 185])).
% 0.22/0.44 tff(189,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n3, n6) | (~less_than(n5, n6)) | (~less_than(n3, n5)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(190,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n5, n6)) | (~less_than(n3, n5)) | less_than(n3, n6)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.22/0.44 tff(191,plain,
% 0.22/0.44 (less_than(n3, n6)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[190, 141, 45, 61])).
% 0.22/0.44 tff(192,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n3, n6) | green(n3, n6) | (~less_than(n3, n6)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n3, n6) | green(n3, n6) | (~less_than(n3, n6)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(193,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n3, n6) | green(n3, n6) | (~less_than(n3, n6)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(194,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n3, n6) | green(n3, n6) | (~less_than(n3, n6))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.22/0.44 tff(195,plain,
% 0.22/0.44 (red(n3, n6) | green(n3, n6)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[194, 89, 191])).
% 0.22/0.44 tff(196,plain,
% 0.22/0.44 (green(n3, n6)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[195, 184])).
% 0.22/0.44 tff(197,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n4, n5)) | (~red(n3, n4)) | (~red(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n4, n5)) | (~red(n3, n4)) | (~red(n3, n5)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(198,plain,
% 0.22/0.44 ((goal | (~red(n3, n4)) | (~red(n4, n5)) | (~red(n3, n5))) <=> (goal | (~red(n4, n5)) | (~red(n3, n4)) | (~red(n3, n5)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(199,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n4)) | (~red(n4, n5)) | (~red(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n4, n5)) | (~red(n3, n4)) | (~red(n3, n5))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[198])).
% 0.22/0.44 tff(200,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n4)) | (~red(n4, n5)) | (~red(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n4, n5)) | (~red(n3, n4)) | (~red(n3, n5)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[199, 197])).
% 0.22/0.44 tff(201,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n4)) | (~red(n4, n5)) | (~red(n3, n5)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(202,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n4, n5)) | (~red(n3, n4)) | (~red(n3, n5))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.22/0.44 tff(203,plain,
% 0.22/0.44 (~red(n3, n5)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[202, 109, 11, 180, 5])).
% 0.22/0.44 tff(204,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n3, n5)) | red(n3, n5) | green(n3, n5))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n3, n5)) | red(n3, n5) | green(n3, n5))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(205,plain,
% 0.22/0.44 ((red(n3, n5) | green(n3, n5) | (~less_than(n3, n5))) <=> ((~less_than(n3, n5)) | red(n3, n5) | green(n3, n5))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(206,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n3, n5) | green(n3, n5) | (~less_than(n3, n5)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n3, n5)) | red(n3, n5) | green(n3, n5)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[205])).
% 0.22/0.44 tff(207,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n3, n5) | green(n3, n5) | (~less_than(n3, n5)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n3, n5)) | red(n3, n5) | green(n3, n5))),
% 0.22/0.44 inference(transitivity,[status(thm)],[206, 204])).
% 0.22/0.44 tff(208,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n3, n5) | green(n3, n5) | (~less_than(n3, n5)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(209,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n3, n5)) | red(n3, n5) | green(n3, n5)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.22/0.44 tff(210,plain,
% 0.22/0.44 (red(n3, n5) | green(n3, n5)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[209, 89, 61])).
% 0.22/0.44 tff(211,plain,
% 0.22/0.44 (green(n3, n5)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[210, 203])).
% 0.22/0.44 tff(212,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n6)) | (~green(n5, n6)) | (~green(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n5, n6)) | (~green(n3, n5)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(213,plain,
% 0.22/0.44 ((goal | (~green(n3, n5)) | (~green(n5, n6)) | (~green(n3, n6))) <=> (goal | (~green(n3, n6)) | (~green(n5, n6)) | (~green(n3, n5)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(214,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n5)) | (~green(n5, n6)) | (~green(n3, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n6)) | (~green(n5, n6)) | (~green(n3, n5))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[213])).
% 0.22/0.44 tff(215,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n5)) | (~green(n5, n6)) | (~green(n3, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n5, n6)) | (~green(n3, n5)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[214, 212])).
% 0.22/0.44 tff(216,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n5)) | (~green(n5, n6)) | (~green(n3, n6)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(217,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n5, n6)) | (~green(n3, n5))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.22/0.44 tff(218,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[217, 24, 11, 1, 211, 196])).
% 0.22/0.44 tff(219,plain,((~red(n3, n4)) | (~green(n5, n6)) | (~red(n4, n6)) | (~red(n4, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(220,plain,
% 0.22/0.44 (~red(n3, n4)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[219, 156, 1, 5])).
% 0.22/0.44 tff(221,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n3, n4)) | red(n3, n4) | green(n3, n4))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n3, n4)) | red(n3, n4) | green(n3, n4))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(222,plain,
% 0.22/0.44 ((red(n3, n4) | green(n3, n4) | (~less_than(n3, n4))) <=> ((~less_than(n3, n4)) | red(n3, n4) | green(n3, n4))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(223,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n3, n4) | green(n3, n4) | (~less_than(n3, n4)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n3, n4)) | red(n3, n4) | green(n3, n4)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[222])).
% 0.22/0.44 tff(224,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n3, n4) | green(n3, n4) | (~less_than(n3, n4)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n3, n4)) | red(n3, n4) | green(n3, n4))),
% 0.22/0.44 inference(transitivity,[status(thm)],[223, 221])).
% 0.22/0.44 tff(225,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n3, n4) | green(n3, n4) | (~less_than(n3, n4)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(226,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n3, n4)) | red(n3, n4) | green(n3, n4)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.22/0.44 tff(227,plain,
% 0.22/0.44 (red(n3, n4) | green(n3, n4)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[226, 54, 89])).
% 0.22/0.44 tff(228,plain,
% 0.22/0.44 (green(n3, n4)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[227, 220])).
% 0.22/0.44 tff(229,assumption,(green(n1, n3)), introduced(assumption)).
% 0.22/0.44 tff(230,assumption,(green(n3, n4)), introduced(assumption)).
% 0.22/0.44 tff(231,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n1, n4)) | (~green(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n1, n4)) | (~green(n1, n3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(232,plain,
% 0.22/0.45 ((goal | (~green(n1, n3)) | (~green(n3, n4)) | (~green(n1, n4))) <=> (goal | (~green(n3, n4)) | (~green(n1, n4)) | (~green(n1, n3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(233,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n4)) | (~green(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n1, n4)) | (~green(n1, n3))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[232])).
% 0.22/0.45 tff(234,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n4)) | (~green(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n1, n4)) | (~green(n1, n3)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[233, 231])).
% 0.22/0.45 tff(235,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n4)) | (~green(n1, n4)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(236,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n1, n4)) | (~green(n1, n3))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.22/0.45 tff(237,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[236, 24, 11, 230, 229, 128])).
% 0.22/0.45 tff(238,plain,((~green(n1, n3)) | (~green(n3, n4)) | (~green(n1, n4))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(239,plain,
% 0.22/0.45 (~green(n1, n3)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[238, 228, 127])).
% 0.22/0.45 tff(240,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n3) | green(n1, n3) | (~less_than(n1, n3)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n1, n3) | green(n1, n3) | (~less_than(n1, n3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(241,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n3) | green(n1, n3) | (~less_than(n1, n3)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(242,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n1, n3) | green(n1, n3) | (~less_than(n1, n3))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.22/0.45 tff(243,plain,
% 0.22/0.45 (red(n1, n3) | green(n1, n3)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[242, 89, 72])).
% 0.22/0.45 tff(244,plain,
% 0.22/0.45 (red(n1, n3)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[243, 239])).
% 0.22/0.45 tff(245,assumption,(red(n1, n3)), introduced(assumption)).
% 0.22/0.45 tff(246,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n5)) | (~red(n3, n5)) | (~red(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n5)) | (~red(n3, n5)) | (~red(n1, n3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(247,plain,
% 0.22/0.45 ((goal | (~red(n1, n3)) | (~red(n3, n5)) | (~red(n1, n5))) <=> (goal | (~red(n1, n5)) | (~red(n3, n5)) | (~red(n1, n3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(248,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n5)) | (~red(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n5)) | (~red(n3, n5)) | (~red(n1, n3))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[247])).
% 0.22/0.45 tff(249,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n5)) | (~red(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n5)) | (~red(n3, n5)) | (~red(n1, n3)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[248, 246])).
% 0.22/0.45 tff(250,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n5)) | (~red(n1, n5)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(251,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n5)) | (~red(n3, n5)) | (~red(n1, n3))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.22/0.45 tff(252,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[251, 109, 11, 245, 2, 95])).
% 0.22/0.45 tff(253,plain,((~red(n3, n5)) | (~red(n1, n3)) | (~red(n1, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(254,plain,
% 0.22/0.45 (~red(n3, n5)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[253, 244, 94])).
% 0.22/0.45 tff(255,plain,
% 0.22/0.45 (green(n3, n5)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[210, 254])).
% 0.22/0.45 tff(256,assumption,(green(n3, n6)), introduced(assumption)).
% 0.22/0.45 tff(257,assumption,(green(n3, n5)), introduced(assumption)).
% 0.22/0.45 tff(258,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[217, 24, 11, 1, 257, 256])).
% 0.22/0.45 tff(259,plain,((~green(n3, n5)) | (~green(n5, n6)) | (~green(n3, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(260,plain,
% 0.22/0.45 (~green(n3, n6)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[259, 255, 1])).
% 0.22/0.45 tff(261,plain,
% 0.22/0.45 (red(n3, n6)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[195, 260])).
% 0.22/0.45 tff(262,assumption,(red(n3, n6)), introduced(assumption)).
% 0.22/0.45 tff(263,assumption,(red(n2, n3)), introduced(assumption)).
% 0.22/0.45 tff(264,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n6)) | (~red(n3, n6)) | (~red(n2, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n2, n6)) | (~red(n3, n6)) | (~red(n2, n3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(265,plain,
% 0.22/0.45 ((goal | (~red(n2, n3)) | (~red(n3, n6)) | (~red(n2, n6))) <=> (goal | (~red(n2, n6)) | (~red(n3, n6)) | (~red(n2, n3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(266,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n3)) | (~red(n3, n6)) | (~red(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n6)) | (~red(n3, n6)) | (~red(n2, n3))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[265])).
% 0.22/0.45 tff(267,plain,
% 0.22/0.45 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n3)) | (~red(n3, n6)) | (~red(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n2, n6)) | (~red(n3, n6)) | (~red(n2, n3)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[266, 264])).
% 0.22/0.45 tff(268,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n3)) | (~red(n3, n6)) | (~red(n2, n6)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(269,plain,
% 0.22/0.45 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n2, n6)) | (~red(n3, n6)) | (~red(n2, n3))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.22/0.45 tff(270,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[269, 109, 11, 263, 6, 262])).
% 0.22/0.45 tff(271,plain,((~red(n2, n3)) | (~red(n2, n6)) | (~red(n3, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(272,plain,
% 0.22/0.45 (~red(n2, n3)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[271, 261, 6])).
% 0.22/0.45 tff(273,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n2, n3)) | red(n2, n3) | green(n2, n3))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n2, n3)) | red(n2, n3) | green(n2, n3))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(274,plain,
% 0.22/0.45 ((red(n2, n3) | green(n2, n3) | (~less_than(n2, n3))) <=> ((~less_than(n2, n3)) | red(n2, n3) | green(n2, n3))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(275,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n3) | green(n2, n3) | (~less_than(n2, n3)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n2, n3)) | red(n2, n3) | green(n2, n3)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[274])).
% 0.22/0.46 tff(276,plain,
% 0.22/0.46 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n3) | green(n2, n3) | (~less_than(n2, n3)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n2, n3)) | red(n2, n3) | green(n2, n3))),
% 0.22/0.46 inference(transitivity,[status(thm)],[275, 273])).
% 0.22/0.46 tff(277,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n3) | green(n2, n3) | (~less_than(n2, n3)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(278,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n2, n3)) | red(n2, n3) | green(n2, n3)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.22/0.46 tff(279,plain,
% 0.22/0.46 (red(n2, n3) | green(n2, n3)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[278, 65, 89])).
% 0.22/0.46 tff(280,plain,
% 0.22/0.46 (green(n2, n3)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[279, 272])).
% 0.22/0.46 tff(281,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n2, n3)) | (~green(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n2, n3)) | (~green(n2, n4)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(282,plain,
% 0.22/0.46 ((goal | (~green(n2, n3)) | (~green(n3, n4)) | (~green(n2, n4))) <=> (goal | (~green(n3, n4)) | (~green(n2, n3)) | (~green(n2, n4)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(283,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n4)) | (~green(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n2, n3)) | (~green(n2, n4))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[282])).
% 0.22/0.46 tff(284,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n4)) | (~green(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n2, n3)) | (~green(n2, n4)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[283, 281])).
% 0.22/0.46 tff(285,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n4)) | (~green(n2, n4)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(286,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n2, n3)) | (~green(n2, n4))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.22/0.46 tff(287,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[286, 24, 11, 280, 228, 179])).
% 0.22/0.46 tff(288,plain,((~green(n1, n6)) | (~red(n2, n6)) | (~green(n5, n6)) | (~red(n4, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(289,plain,
% 0.22/0.46 (~green(n1, n6)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[288, 6, 1, 5])).
% 0.22/0.46 tff(290,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n4, n6)) | (~less_than(n1, n4)) | less_than(n1, n6))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n6)) | (~less_than(n1, n4)) | less_than(n1, n6))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(291,plain,
% 0.22/0.46 ((less_than(n1, n6) | (~less_than(n4, n6)) | (~less_than(n1, n4))) <=> ((~less_than(n4, n6)) | (~less_than(n1, n4)) | less_than(n1, n6))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(292,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n6) | (~less_than(n4, n6)) | (~less_than(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n4, n6)) | (~less_than(n1, n4)) | less_than(n1, n6)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[291])).
% 0.22/0.46 tff(293,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n6) | (~less_than(n4, n6)) | (~less_than(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n6)) | (~less_than(n1, n4)) | less_than(n1, n6))),
% 0.22/0.46 inference(transitivity,[status(thm)],[292, 290])).
% 0.22/0.46 tff(294,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n1, n6) | (~less_than(n4, n6)) | (~less_than(n1, n4)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(295,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n6)) | (~less_than(n1, n4)) | less_than(n1, n6)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.22/0.46 tff(296,plain,
% 0.22/0.46 (less_than(n1, n6)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[295, 45, 148, 122])).
% 0.22/0.46 tff(297,plain,
% 0.22/0.46 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n6) | green(n1, n6) | (~less_than(n1, n6)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n1, n6) | green(n1, n6) | (~less_than(n1, n6)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(298,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n6) | green(n1, n6) | (~less_than(n1, n6)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(299,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n1, n6) | green(n1, n6) | (~less_than(n1, n6))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.22/0.46 tff(300,plain,
% 0.22/0.46 (red(n1, n6) | green(n1, n6)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[299, 89, 296])).
% 0.22/0.46 tff(301,plain,
% 0.22/0.46 (red(n1, n6)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[300, 289])).
% 0.22/0.46 tff(302,plain,
% 0.22/0.46 (~green(n3, n5)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[259, 256, 1])).
% 0.22/0.46 tff(303,plain,
% 0.22/0.46 (red(n3, n5)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[210, 302])).
% 0.22/0.46 tff(304,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n4, n6)) | (~green(n3, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n4, n6)) | (~green(n3, n6)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(305,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n4, n6)) | (~green(n3, n6)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(306,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n4, n6)) | (~green(n3, n6))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.22/0.46 tff(307,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[306, 24, 11, 230, 129, 256])).
% 0.22/0.46 tff(308,plain,((~green(n3, n4)) | (~green(n4, n6)) | (~green(n3, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(309,plain,
% 0.22/0.46 (~green(n3, n4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[308, 256, 129])).
% 0.22/0.46 tff(310,plain,
% 0.22/0.46 (red(n3, n4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[227, 309])).
% 0.22/0.46 tff(311,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[202, 109, 11, 310, 5, 303])).
% 0.22/0.46 tff(312,plain,((~green(n3, n6)) | (~red(n4, n5)) | (~green(n4, n6)) | (~green(n5, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(313,plain,
% 0.22/0.46 (~green(n4, n6)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[312, 256, 5, 1])).
% 0.22/0.46 tff(314,plain,
% 0.22/0.46 (red(n4, n6)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[155, 313])).
% 0.22/0.46 tff(315,plain,
% 0.22/0.46 (~red(n2, n4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[166, 314, 6])).
% 0.22/0.46 tff(316,plain,
% 0.22/0.46 (green(n2, n4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[178, 315])).
% 0.22/0.46 tff(317,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[202, 109, 11, 180, 5, 2])).
% 0.22/0.46 tff(318,plain,((~red(n3, n4)) | (~red(n4, n5)) | (~red(n3, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(319,plain,
% 0.22/0.46 (~red(n3, n4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[318, 303, 5])).
% 0.22/0.46 tff(320,plain,
% 0.22/0.46 (green(n3, n4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[227, 319])).
% 0.22/0.46 tff(321,assumption,(red(n1, n6)), introduced(assumption)).
% 0.22/0.46 tff(322,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n6)) | (~red(n1, n4)) | (~red(n4, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n6)) | (~red(n1, n4)) | (~red(n4, n6)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(323,plain,
% 0.22/0.46 ((goal | (~red(n1, n4)) | (~red(n4, n6)) | (~red(n1, n6))) <=> (goal | (~red(n1, n6)) | (~red(n1, n4)) | (~red(n4, n6)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(324,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n4)) | (~red(n4, n6)) | (~red(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n6)) | (~red(n1, n4)) | (~red(n4, n6))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[323])).
% 0.22/0.46 tff(325,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n4)) | (~red(n4, n6)) | (~red(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n6)) | (~red(n1, n4)) | (~red(n4, n6)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[324, 322])).
% 0.22/0.46 tff(326,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n4)) | (~red(n4, n6)) | (~red(n1, n6)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(327,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n6)) | (~red(n1, n4)) | (~red(n4, n6))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.22/0.46 tff(328,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[327, 109, 11, 157, 96, 321])).
% 0.22/0.46 tff(329,plain,((~red(n1, n4)) | (~red(n4, n6)) | (~red(n1, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(330,plain,
% 0.22/0.46 (~red(n1, n4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[329, 314, 301])).
% 0.22/0.46 tff(331,plain,
% 0.22/0.46 (green(n1, n4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[126, 330])).
% 0.22/0.46 tff(332,plain,
% 0.22/0.46 (~green(n1, n3)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[238, 331, 320])).
% 0.22/0.46 tff(333,plain,
% 0.22/0.46 (red(n1, n3)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[243, 332])).
% 0.22/0.46 tff(334,assumption,(green(n1, n2)), introduced(assumption)).
% 0.22/0.46 tff(335,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n2, n4)) | (~green(n1, n2)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n4)) | (~green(n2, n4)) | (~green(n1, n2)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(336,plain,
% 0.22/0.46 ((goal | (~green(n1, n2)) | (~green(n2, n4)) | (~green(n1, n4))) <=> (goal | (~green(n1, n4)) | (~green(n2, n4)) | (~green(n1, n2)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(337,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n4)) | (~green(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n2, n4)) | (~green(n1, n2))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[336])).
% 0.22/0.46 tff(338,plain,
% 0.22/0.46 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n4)) | (~green(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n4)) | (~green(n2, n4)) | (~green(n1, n2)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[337, 335])).
% 0.22/0.46 tff(339,plain,
% 0.22/0.46 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n4)) | (~green(n1, n4)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(340,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n4)) | (~green(n2, n4)) | (~green(n1, n2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.22/0.47 tff(341,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[340, 24, 11, 334, 4, 128])).
% 0.22/0.47 tff(342,plain,((~green(n1, n2)) | (~green(n2, n4)) | (~green(n1, n4))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(343,plain,
% 0.22/0.47 (~green(n1, n2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[342, 316, 331])).
% 0.22/0.47 tff(344,plain,
% 0.22/0.47 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n1, n2)) | red(n1, n2) | green(n1, n2))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n1, n2)) | red(n1, n2) | green(n1, n2))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(345,plain,
% 0.22/0.47 ((red(n1, n2) | green(n1, n2) | (~less_than(n1, n2))) <=> ((~less_than(n1, n2)) | red(n1, n2) | green(n1, n2))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(346,plain,
% 0.22/0.47 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n2) | green(n1, n2) | (~less_than(n1, n2)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n1, n2)) | red(n1, n2) | green(n1, n2)))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[345])).
% 0.22/0.47 tff(347,plain,
% 0.22/0.47 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n2) | green(n1, n2) | (~less_than(n1, n2)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n1, n2)) | red(n1, n2) | green(n1, n2))),
% 0.22/0.47 inference(transitivity,[status(thm)],[346, 344])).
% 0.22/0.47 tff(348,plain,
% 0.22/0.47 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n1, n2) | green(n1, n2) | (~less_than(n1, n2)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(349,plain,
% 0.22/0.47 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n1, n2)) | red(n1, n2) | green(n1, n2)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.22/0.47 tff(350,plain,
% 0.22/0.47 (red(n1, n2) | green(n1, n2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[349, 68, 89])).
% 0.22/0.47 tff(351,plain,
% 0.22/0.47 (red(n1, n2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[350, 343])).
% 0.22/0.47 tff(352,assumption,(red(n1, n2)), introduced(assumption)).
% 0.22/0.47 tff(353,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n1, n3)) | (~red(n2, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n3)) | (~red(n2, n3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(354,plain,
% 0.22/0.47 ((goal | (~red(n1, n2)) | (~red(n2, n3)) | (~red(n1, n3))) <=> (goal | (~red(n1, n2)) | (~red(n1, n3)) | (~red(n2, n3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(355,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n3)) | (~red(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n1, n3)) | (~red(n2, n3))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[354])).
% 0.22/0.47 tff(356,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n3)) | (~red(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n3)) | (~red(n2, n3)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[355, 353])).
% 0.22/0.47 tff(357,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n3)) | (~red(n1, n3)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(358,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n3)) | (~red(n2, n3))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.22/0.47 tff(359,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[358, 109, 11, 352, 263, 245])).
% 0.22/0.47 tff(360,plain,((~red(n1, n2)) | (~red(n2, n3)) | (~red(n1, n3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(361,plain,
% 0.22/0.47 (~red(n2, n3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[360, 351, 333])).
% 0.22/0.47 tff(362,plain,
% 0.22/0.47 (green(n2, n3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[279, 361])).
% 0.22/0.47 tff(363,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[286, 24, 11, 362, 320, 316])).
% 0.22/0.47 tff(364,plain,((~green(n3, n6)) | (~red(n2, n6)) | (~red(n4, n5)) | (~green(n5, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(365,plain,
% 0.22/0.47 (~green(n3, n6)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[364, 6, 5, 1])).
% 0.22/0.47 tff(366,plain,
% 0.22/0.47 (red(n3, n6)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[195, 365])).
% 0.22/0.47 tff(367,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n6)) | (~red(n3, n6)) | (~red(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n6)) | (~red(n3, n6)) | (~red(n1, n3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(368,plain,
% 0.22/0.47 ((goal | (~red(n1, n3)) | (~red(n3, n6)) | (~red(n1, n6))) <=> (goal | (~red(n1, n6)) | (~red(n3, n6)) | (~red(n1, n3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(369,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n6)) | (~red(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n6)) | (~red(n3, n6)) | (~red(n1, n3))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[368])).
% 0.22/0.47 tff(370,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n6)) | (~red(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n6)) | (~red(n3, n6)) | (~red(n1, n3)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[369, 367])).
% 0.22/0.47 tff(371,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n6)) | (~red(n1, n6)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(372,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n6)) | (~red(n3, n6)) | (~red(n1, n3))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.22/0.47 tff(373,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[372, 109, 11, 245, 262, 321])).
% 0.22/0.47 tff(374,plain,((~red(n1, n3)) | (~red(n3, n6)) | (~red(n1, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(375,plain,
% 0.22/0.47 (~red(n1, n3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[374, 262, 321])).
% 0.22/0.47 tff(376,plain,
% 0.22/0.47 (green(n1, n3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[243, 375])).
% 0.22/0.47 tff(377,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n5)) | (~green(n1, n3)) | (~green(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n5)) | (~green(n1, n3)) | (~green(n3, n5)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(378,plain,
% 0.22/0.47 ((goal | (~green(n1, n3)) | (~green(n3, n5)) | (~green(n1, n5))) <=> (goal | (~green(n1, n5)) | (~green(n1, n3)) | (~green(n3, n5)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(379,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n5)) | (~green(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n5)) | (~green(n1, n3)) | (~green(n3, n5))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[378])).
% 0.22/0.47 tff(380,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n5)) | (~green(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n5)) | (~green(n1, n3)) | (~green(n3, n5)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[379, 377])).
% 0.22/0.47 tff(381,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n5)) | (~green(n1, n5)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(382,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n5)) | (~green(n1, n3)) | (~green(n3, n5))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.22/0.47 tff(383,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[382, 24, 11, 229, 257, 8])).
% 0.22/0.47 tff(384,plain,((~green(n1, n3)) | (~green(n3, n5)) | (~green(n1, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(385,plain,
% 0.22/0.47 (~green(n3, n5)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[384, 376, 8])).
% 0.22/0.47 tff(386,plain,
% 0.22/0.47 (red(n3, n5)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[210, 385])).
% 0.22/0.47 tff(387,plain,
% 0.22/0.47 (~red(n3, n4)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[318, 386, 5])).
% 0.22/0.47 tff(388,plain,
% 0.22/0.47 (green(n3, n4)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[227, 387])).
% 0.22/0.47 tff(389,plain,
% 0.22/0.47 (~green(n1, n4)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[238, 388, 376])).
% 0.22/0.47 tff(390,plain,
% 0.22/0.47 (red(n1, n4)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[126, 389])).
% 0.22/0.47 tff(391,plain,
% 0.22/0.47 (~red(n2, n3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[271, 262, 6])).
% 0.22/0.47 tff(392,plain,
% 0.22/0.47 (green(n2, n3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[279, 391])).
% 0.22/0.47 tff(393,plain,
% 0.22/0.47 (~green(n2, n4)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[286, 24, 11, 392, 388])).
% 0.22/0.47 tff(394,plain,
% 0.22/0.47 (red(n2, n4)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[178, 393])).
% 0.22/0.47 tff(395,assumption,(green(n2, n3)), introduced(assumption)).
% 0.22/0.47 tff(396,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n2, n3)) | (~green(n1, n2)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n3)) | (~green(n2, n3)) | (~green(n1, n2)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(397,plain,
% 0.22/0.47 ((goal | (~green(n1, n2)) | (~green(n2, n3)) | (~green(n1, n3))) <=> (goal | (~green(n1, n3)) | (~green(n2, n3)) | (~green(n1, n2)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(398,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n3)) | (~green(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n2, n3)) | (~green(n1, n2))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[397])).
% 0.22/0.47 tff(399,plain,
% 0.22/0.47 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n3)) | (~green(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n3)) | (~green(n2, n3)) | (~green(n1, n2)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[398, 396])).
% 0.22/0.47 tff(400,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n3)) | (~green(n1, n3)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(401,plain,
% 0.22/0.47 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n3)) | (~green(n2, n3)) | (~green(n1, n2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.22/0.47 tff(402,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[401, 24, 11, 334, 395, 229])).
% 0.22/0.47 tff(403,plain,((~green(n1, n2)) | (~green(n2, n3)) | (~green(n1, n3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(404,plain,
% 0.22/0.47 (~green(n1, n2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[403, 392, 376])).
% 0.22/0.47 tff(405,plain,
% 0.22/0.47 (red(n1, n2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[350, 404])).
% 0.22/0.48 tff(406,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n1, n4)) | (~red(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n4)) | (~red(n2, n4)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(407,plain,
% 0.22/0.48 ((goal | (~red(n1, n2)) | (~red(n2, n4)) | (~red(n1, n4))) <=> (goal | (~red(n1, n2)) | (~red(n1, n4)) | (~red(n2, n4)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(408,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n4)) | (~red(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n1, n4)) | (~red(n2, n4))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[407])).
% 0.22/0.48 tff(409,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n4)) | (~red(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n4)) | (~red(n2, n4)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[408, 406])).
% 0.22/0.48 tff(410,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n4)) | (~red(n1, n4)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(411,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n4)) | (~red(n2, n4))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.22/0.48 tff(412,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[411, 109, 11, 405, 394, 390])).
% 0.22/0.48 tff(413,plain,((~red(n3, n6)) | (~red(n4, n5)) | (~green(n1, n5)) | (~red(n1, n6)) | (~red(n2, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(414,plain,
% 0.22/0.48 (~green(n1, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[413, 366, 5, 301, 6])).
% 0.22/0.48 tff(415,plain,
% 0.22/0.48 (red(n1, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[93, 414])).
% 0.22/0.48 tff(416,plain,
% 0.22/0.48 (~red(n1, n3)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[374, 366, 301])).
% 0.22/0.48 tff(417,plain,
% 0.22/0.48 (green(n1, n3)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[243, 416])).
% 0.22/0.48 tff(418,plain,
% 0.22/0.48 (~red(n2, n3)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[271, 366, 6])).
% 0.22/0.48 tff(419,plain,
% 0.22/0.48 (green(n2, n3)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[279, 418])).
% 0.22/0.48 tff(420,plain,
% 0.22/0.48 (~green(n1, n2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[403, 419, 417])).
% 0.22/0.48 tff(421,plain,
% 0.22/0.48 (red(n1, n2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[350, 420])).
% 0.22/0.48 tff(422,assumption,(red(n2, n5)), introduced(assumption)).
% 0.22/0.48 tff(423,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n1, n5)) | (~red(n2, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n5)) | (~red(n2, n5)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(424,plain,
% 0.22/0.48 ((goal | (~red(n1, n2)) | (~red(n2, n5)) | (~red(n1, n5))) <=> (goal | (~red(n1, n2)) | (~red(n1, n5)) | (~red(n2, n5)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(425,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n5)) | (~red(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n1, n5)) | (~red(n2, n5))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[424])).
% 0.22/0.48 tff(426,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n5)) | (~red(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n5)) | (~red(n2, n5)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[425, 423])).
% 0.22/0.48 tff(427,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n2)) | (~red(n2, n5)) | (~red(n1, n5)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(428,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n2)) | (~red(n1, n5)) | (~red(n2, n5))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.22/0.48 tff(429,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[428, 109, 11, 352, 95, 422])).
% 0.22/0.48 tff(430,plain,((~red(n2, n5)) | (~red(n1, n2)) | (~red(n1, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(431,plain,
% 0.22/0.48 (~red(n2, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[430, 421, 415])).
% 0.22/0.48 tff(432,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n4, n5)) | (~less_than(n2, n4)) | less_than(n2, n5))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n5)) | (~less_than(n2, n4)) | less_than(n2, n5))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(433,plain,
% 0.22/0.48 ((less_than(n2, n5) | (~less_than(n4, n5)) | (~less_than(n2, n4))) <=> ((~less_than(n4, n5)) | (~less_than(n2, n4)) | less_than(n2, n5))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(434,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n5) | (~less_than(n4, n5)) | (~less_than(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n4, n5)) | (~less_than(n2, n4)) | less_than(n2, n5)))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[433])).
% 0.22/0.48 tff(435,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n5) | (~less_than(n4, n5)) | (~less_than(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n5)) | (~less_than(n2, n4)) | less_than(n2, n5))),
% 0.22/0.48 inference(transitivity,[status(thm)],[434, 432])).
% 0.22/0.48 tff(436,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n5) | (~less_than(n4, n5)) | (~less_than(n2, n4)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(437,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n4, n5)) | (~less_than(n2, n4)) | less_than(n2, n5)),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.22/0.48 tff(438,plain,
% 0.22/0.48 (less_than(n2, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[437, 50, 45, 174])).
% 0.22/0.48 tff(439,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n5) | green(n2, n5) | (~less_than(n2, n5)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n2, n5) | green(n2, n5) | (~less_than(n2, n5)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(440,plain,
% 0.22/0.48 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n5) | green(n2, n5) | (~less_than(n2, n5)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(441,plain,
% 0.22/0.48 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n2, n5) | green(n2, n5) | (~less_than(n2, n5))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.22/0.48 tff(442,plain,
% 0.22/0.48 (red(n2, n5) | green(n2, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[441, 89, 438])).
% 0.22/0.48 tff(443,plain,
% 0.22/0.48 (green(n2, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[442, 431])).
% 0.22/0.48 tff(444,plain,
% 0.22/0.48 (~red(n1, n4)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[114, 415, 5])).
% 0.22/0.48 tff(445,plain,
% 0.22/0.48 (green(n1, n4)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[126, 444])).
% 0.22/0.48 tff(446,plain,
% 0.22/0.48 (~green(n3, n4)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[238, 445, 417])).
% 0.22/0.48 tff(447,plain,
% 0.22/0.48 (red(n3, n4)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[227, 446])).
% 0.22/0.48 tff(448,plain,
% 0.22/0.48 (~red(n3, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[318, 447, 5])).
% 0.22/0.48 tff(449,plain,
% 0.22/0.48 (green(n3, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[210, 448])).
% 0.22/0.48 tff(450,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n5)) | (~green(n3, n5)) | (~green(n2, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n2, n5)) | (~green(n3, n5)) | (~green(n2, n3)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(451,plain,
% 0.22/0.48 ((goal | (~green(n2, n3)) | (~green(n3, n5)) | (~green(n2, n5))) <=> (goal | (~green(n2, n5)) | (~green(n3, n5)) | (~green(n2, n3)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(452,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n5)) | (~green(n2, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n5)) | (~green(n3, n5)) | (~green(n2, n3))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[451])).
% 0.22/0.48 tff(453,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n5)) | (~green(n2, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n2, n5)) | (~green(n3, n5)) | (~green(n2, n3)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[452, 450])).
% 0.22/0.48 tff(454,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n5)) | (~green(n2, n5)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(455,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n2, n5)) | (~green(n3, n5)) | (~green(n2, n3))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.22/0.48 tff(456,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[455, 24, 11, 419, 449, 443])).
% 0.22/0.48 tff(457,plain,((~red(n2, n6)) | (~red(n4, n5)) | (~green(n5, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(458,plain,
% 0.22/0.48 (~red(n2, n6)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[457, 1, 5])).
% 0.22/0.48 tff(459,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n2, n4)) | less_than(n2, n6) | (~less_than(n4, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n2, n4)) | less_than(n2, n6) | (~less_than(n4, n6)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(460,plain,
% 0.22/0.48 ((less_than(n2, n6) | (~less_than(n4, n6)) | (~less_than(n2, n4))) <=> ((~less_than(n2, n4)) | less_than(n2, n6) | (~less_than(n4, n6)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(461,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n6) | (~less_than(n4, n6)) | (~less_than(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | ((~less_than(n2, n4)) | less_than(n2, n6) | (~less_than(n4, n6))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[460])).
% 0.22/0.48 tff(462,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n6) | (~less_than(n4, n6)) | (~less_than(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n2, n4)) | less_than(n2, n6) | (~less_than(n4, n6)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[461, 459])).
% 0.22/0.48 tff(463,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (less_than(n2, n6) | (~less_than(n4, n6)) | (~less_than(n2, n4)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(464,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (less_than(A, C) | (~less_than(B, C)) | (~less_than(A, B)))) | (~less_than(n2, n4)) | less_than(n2, n6) | (~less_than(n4, n6))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.22/0.48 tff(465,plain,
% 0.22/0.48 (less_than(n2, n6)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[464, 45, 174, 148])).
% 0.22/0.48 tff(466,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n6) | green(n2, n6) | (~less_than(n2, n6)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n2, n6) | green(n2, n6) | (~less_than(n2, n6)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(467,plain,
% 0.22/0.48 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n2, n6) | green(n2, n6) | (~less_than(n2, n6)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(468,plain,
% 0.22/0.48 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | red(n2, n6) | green(n2, n6) | (~less_than(n2, n6))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.22/0.48 tff(469,plain,
% 0.22/0.48 (red(n2, n6) | green(n2, n6)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[468, 89, 465])).
% 0.22/0.48 tff(470,plain,
% 0.22/0.48 (green(n2, n6)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[469, 458])).
% 0.22/0.48 tff(471,assumption,(green(n2, n6)), introduced(assumption)).
% 0.22/0.48 tff(472,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n5, n6)) | (~green(n2, n5)) | (~green(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n5, n6)) | (~green(n2, n5)) | (~green(n2, n6)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(473,plain,
% 0.22/0.48 ((goal | (~green(n2, n5)) | (~green(n5, n6)) | (~green(n2, n6))) <=> (goal | (~green(n5, n6)) | (~green(n2, n5)) | (~green(n2, n6)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(474,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n5)) | (~green(n5, n6)) | (~green(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n5, n6)) | (~green(n2, n5)) | (~green(n2, n6))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[473])).
% 0.22/0.48 tff(475,plain,
% 0.22/0.48 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n5)) | (~green(n5, n6)) | (~green(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n5, n6)) | (~green(n2, n5)) | (~green(n2, n6)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[474, 472])).
% 0.22/0.48 tff(476,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n5)) | (~green(n5, n6)) | (~green(n2, n6)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(477,plain,
% 0.22/0.48 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n5, n6)) | (~green(n2, n5)) | (~green(n2, n6))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.22/0.48 tff(478,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[477, 24, 11, 1, 3, 471])).
% 0.22/0.48 tff(479,plain,((~green(n2, n5)) | (~green(n5, n6)) | (~green(n2, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(480,plain,
% 0.22/0.48 (~green(n2, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[479, 1, 470])).
% 0.22/0.48 tff(481,plain,
% 0.22/0.48 (red(n2, n5)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[442, 480])).
% 0.22/0.48 tff(482,plain,
% 0.22/0.49 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n4, n5)) | (~red(n2, n5)) | (~red(n2, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n4, n5)) | (~red(n2, n5)) | (~red(n2, n4)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(483,plain,
% 0.22/0.49 ((goal | (~red(n2, n4)) | (~red(n4, n5)) | (~red(n2, n5))) <=> (goal | (~red(n4, n5)) | (~red(n2, n5)) | (~red(n2, n4)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(484,plain,
% 0.22/0.49 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n4)) | (~red(n4, n5)) | (~red(n2, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n4, n5)) | (~red(n2, n5)) | (~red(n2, n4))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[483])).
% 0.22/0.49 tff(485,plain,
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% 0.22/0.49 inference(transitivity,[status(thm)],[484, 482])).
% 0.22/0.49 tff(486,plain,
% 0.22/0.49 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n4)) | (~red(n4, n5)) | (~red(n2, n5)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(487,plain,
% 0.22/0.49 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n4, n5)) | (~red(n2, n5)) | (~red(n2, n4))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.22/0.49 tff(488,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[487, 109, 11, 5, 158, 422])).
% 0.22/0.49 tff(489,plain,((~red(n2, n4)) | (~red(n4, n5)) | (~red(n2, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.49 tff(490,plain,
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% 0.22/0.49 tff(492,plain,
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% 0.22/0.49 tff(493,plain,
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% 0.22/0.49 inference(unit_resolution,[status(thm)],[227, 492])).
% 0.22/0.49 tff(494,plain,
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% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(495,plain,
% 0.22/0.49 ((goal | (~red(n2, n3)) | (~red(n3, n5)) | (~red(n2, n5))) <=> (goal | (~red(n2, n5)) | (~red(n3, n5)) | (~red(n2, n3)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(496,plain,
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% 0.22/0.49 inference(transitivity,[status(thm)],[496, 494])).
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% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(499,plain,
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% 0.22/0.49 tff(505,plain,((~red(n3, n5)) | (~red(n2, n5)) | (~red(n4, n5))), inference(lemma,lemma(discharge,[]))).
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% 0.22/0.49 (~green(n3, n6)),
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% 0.22/0.49 inference(unit_resolution,[status(thm)],[442, 520])).
% 0.22/0.49 tff(522,plain,
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% 0.22/0.49 tff(523,plain,((~green(n2, n3)) | (~green(n3, n5)) | (~green(n1, n3))), inference(lemma,lemma(discharge,[]))).
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% 0.22/0.49 tff(526,plain,
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% 0.22/0.49 inference(rewrite,[status(thm)],[])).
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% 0.22/0.49 inference(rewrite,[status(thm)],[])).
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% 0.22/0.49 inference(monotonicity,[status(thm)],[527])).
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% 0.22/0.49 inference(transitivity,[status(thm)],[528, 526])).
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% 0.22/0.49 inference(rewrite,[status(thm)],[])).
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% 0.22/0.49 inference(rewrite,[status(thm)],[])).
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% 0.22/0.49 inference(monotonicity,[status(thm)],[535])).
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% 0.22/0.49 inference(transitivity,[status(thm)],[536, 534])).
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% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
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% 0.22/0.49 inference(rewrite,[status(thm)],[])).
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% 0.22/0.49 inference(transitivity,[status(thm)],[550, 548])).
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% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
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% 0.22/0.50 tff(592,plain,
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% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(593,plain,
% 0.22/0.50 ((goal | (~red(n2, n5)) | (~red(n5, n6)) | (~red(n2, n6))) <=> (goal | (~red(n2, n6)) | (~red(n2, n5)) | (~red(n5, n6)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(594,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n5)) | (~red(n5, n6)) | (~red(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n6)) | (~red(n2, n5)) | (~red(n5, n6))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[593])).
% 0.22/0.50 tff(595,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n5)) | (~red(n5, n6)) | (~red(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n2, n6)) | (~red(n2, n5)) | (~red(n5, n6)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[594, 592])).
% 0.22/0.50 tff(596,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n2, n5)) | (~red(n5, n6)) | (~red(n2, n6)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(597,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n2, n6)) | (~red(n2, n5)) | (~red(n5, n6))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.22/0.50 tff(598,plain,
% 0.22/0.50 (~red(n2, n6)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[597, 109, 11, 568, 422])).
% 0.22/0.50 tff(599,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[469, 598, 591])).
% 0.22/0.50 tff(600,plain,((~red(n2, n5)) | (~red(n4, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(601,plain,
% 0.22/0.50 (~red(n2, n5)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[600, 5])).
% 0.22/0.50 tff(602,plain,
% 0.22/0.50 (green(n2, n5)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[442, 601])).
% 0.22/0.50 tff(603,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n5)) | (~green(n2, n5)) | (~green(n1, n2)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n5)) | (~green(n2, n5)) | (~green(n1, n2)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(604,plain,
% 0.22/0.50 ((goal | (~green(n1, n2)) | (~green(n2, n5)) | (~green(n1, n5))) <=> (goal | (~green(n1, n5)) | (~green(n2, n5)) | (~green(n1, n2)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(605,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n5)) | (~green(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n5)) | (~green(n2, n5)) | (~green(n1, n2))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[604])).
% 0.22/0.50 tff(606,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n5)) | (~green(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n5)) | (~green(n2, n5)) | (~green(n1, n2)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[605, 603])).
% 0.22/0.50 tff(607,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n2)) | (~green(n2, n5)) | (~green(n1, n5)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(608,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n5)) | (~green(n2, n5)) | (~green(n1, n2))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.22/0.50 tff(609,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[608, 24, 11, 334, 8, 3])).
% 0.22/0.50 tff(610,plain,((~green(n2, n5)) | (~green(n1, n2)) | (~green(n1, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(611,plain,
% 0.22/0.50 (~green(n1, n2)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[610, 3, 8])).
% 0.22/0.50 tff(612,plain,
% 0.22/0.50 (red(n1, n2)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[350, 611])).
% 0.22/0.50 tff(613,plain,
% 0.22/0.50 (~green(n1, n3)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[384, 257, 8])).
% 0.22/0.50 tff(614,plain,
% 0.22/0.50 (red(n1, n3)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[243, 613])).
% 0.22/0.50 tff(615,plain,
% 0.22/0.50 (~red(n2, n3)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[360, 614, 612])).
% 0.22/0.50 tff(616,plain,
% 0.22/0.50 (green(n2, n3)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[279, 615])).
% 0.22/0.50 tff(617,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[455, 24, 11, 616, 257, 3])).
% 0.22/0.50 tff(618,plain,((~green(n3, n5)) | (~green(n2, n5)) | (~green(n1, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(619,plain,
% 0.22/0.50 (~green(n3, n5)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[618, 602, 590])).
% 0.22/0.50 tff(620,plain,
% 0.22/0.50 (red(n3, n5)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[210, 619])).
% 0.22/0.50 tff(621,plain,
% 0.22/0.50 (~red(n3, n4)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[318, 620, 5])).
% 0.22/0.50 tff(622,plain,
% 0.22/0.50 (green(n3, n4)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[227, 621])).
% 0.22/0.50 tff(623,plain,
% 0.22/0.50 (~green(n3, n6)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[308, 622, 576])).
% 0.22/0.50 tff(624,plain,
% 0.22/0.50 (red(n3, n6)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[195, 623])).
% 0.22/0.50 tff(625,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n5)) | (~red(n3, n6)) | (~red(n5, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n3, n5)) | (~red(n3, n6)) | (~red(n5, n6)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(626,plain,
% 0.22/0.50 ((goal | (~red(n3, n5)) | (~red(n5, n6)) | (~red(n3, n6))) <=> (goal | (~red(n3, n5)) | (~red(n3, n6)) | (~red(n5, n6)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(627,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n5)) | (~red(n5, n6)) | (~red(n3, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n5)) | (~red(n3, n6)) | (~red(n5, n6))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[626])).
% 0.22/0.50 tff(628,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n5)) | (~red(n5, n6)) | (~red(n3, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n3, n5)) | (~red(n3, n6)) | (~red(n5, n6)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[627, 625])).
% 0.22/0.50 tff(629,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n3, n5)) | (~red(n5, n6)) | (~red(n3, n6)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(630,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n3, n5)) | (~red(n3, n6)) | (~red(n5, n6))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.22/0.50 tff(631,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[630, 109, 11, 568, 620, 624])).
% 0.22/0.50 tff(632,plain,(~red(n4, n5)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(633,plain,
% 0.22/0.50 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n4, n5)) | red(n4, n5) | green(n4, n5))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n4, n5)) | red(n4, n5) | green(n4, n5))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(634,plain,
% 0.22/0.50 ((red(n4, n5) | green(n4, n5) | (~less_than(n4, n5))) <=> ((~less_than(n4, n5)) | red(n4, n5) | green(n4, n5))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(635,plain,
% 0.22/0.50 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n4, n5) | green(n4, n5) | (~less_than(n4, n5)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | ((~less_than(n4, n5)) | red(n4, n5) | green(n4, n5)))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[634])).
% 0.22/0.50 tff(636,plain,
% 0.22/0.50 (((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n4, n5) | green(n4, n5) | (~less_than(n4, n5)))) <=> ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n4, n5)) | red(n4, n5) | green(n4, n5))),
% 0.22/0.50 inference(transitivity,[status(thm)],[635, 633])).
% 0.22/0.50 tff(637,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (red(n4, n5) | green(n4, n5) | (~less_than(n4, n5)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(638,plain,
% 0.22/0.50 ((~![A: $i, B: $i] : (red(A, B) | green(A, B) | (~less_than(A, B)))) | (~less_than(n4, n5)) | red(n4, n5) | green(n4, n5)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.22/0.50 tff(639,plain,
% 0.22/0.50 (red(n4, n5) | green(n4, n5)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[638, 50, 89])).
% 0.22/0.50 tff(640,plain,
% 0.22/0.50 (green(n4, n5)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[639, 632])).
% 0.22/0.50 tff(641,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n5)) | (~green(n2, n4)) | (~green(n4, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n2, n5)) | (~green(n2, n4)) | (~green(n4, n5)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(642,plain,
% 0.22/0.50 ((goal | (~green(n2, n4)) | (~green(n4, n5)) | (~green(n2, n5))) <=> (goal | (~green(n2, n5)) | (~green(n2, n4)) | (~green(n4, n5)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(643,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n4)) | (~green(n4, n5)) | (~green(n2, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n5)) | (~green(n2, n4)) | (~green(n4, n5))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[642])).
% 0.22/0.50 tff(644,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n4)) | (~green(n4, n5)) | (~green(n2, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n2, n5)) | (~green(n2, n4)) | (~green(n4, n5)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[643, 641])).
% 0.22/0.50 tff(645,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n4)) | (~green(n4, n5)) | (~green(n2, n5)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(646,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n2, n5)) | (~green(n2, n4)) | (~green(n4, n5))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.22/0.50 tff(647,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[646, 24, 11, 640, 4, 3])).
% 0.22/0.50 tff(648,plain,((~green(n2, n4)) | (~green(n2, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(649,plain,
% 0.22/0.50 (~green(n2, n4)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[648, 3])).
% 0.22/0.50 tff(650,plain,
% 0.22/0.50 (red(n2, n4)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[178, 649])).
% 0.22/0.50 tff(651,plain,
% 0.22/0.50 (~green(n1, n2)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[610, 8, 3])).
% 0.22/0.50 tff(652,plain,
% 0.22/0.50 (red(n1, n2)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[350, 651])).
% 0.22/0.50 tff(653,plain,
% 0.22/0.50 (~red(n1, n4)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[411, 109, 11, 652, 650])).
% 0.22/0.50 tff(654,plain,
% 0.22/0.50 (green(n1, n4)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[126, 653])).
% 0.22/0.50 tff(655,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n1, n5)) | (~green(n4, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n4)) | (~green(n1, n5)) | (~green(n4, n5)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(656,plain,
% 0.22/0.50 ((goal | (~green(n1, n4)) | (~green(n4, n5)) | (~green(n1, n5))) <=> (goal | (~green(n1, n4)) | (~green(n1, n5)) | (~green(n4, n5)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(657,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n4, n5)) | (~green(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n1, n5)) | (~green(n4, n5))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[656])).
% 0.22/0.50 tff(658,plain,
% 0.22/0.50 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n4, n5)) | (~green(n1, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n4)) | (~green(n1, n5)) | (~green(n4, n5)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[657, 655])).
% 0.22/0.50 tff(659,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n4)) | (~green(n4, n5)) | (~green(n1, n5)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(660,plain,
% 0.22/0.50 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n1, n4)) | (~green(n1, n5)) | (~green(n4, n5))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.22/0.50 tff(661,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[660, 24, 11, 640, 654, 8])).
% 0.22/0.50 tff(662,plain,((~green(n1, n5)) | (~green(n2, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(663,plain,
% 0.22/0.50 (~green(n1, n5)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[662, 3])).
% 0.22/0.50 tff(664,plain,
% 0.22/0.50 (red(n1, n5)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[93, 663])).
% 0.22/0.50 tff(665,assumption,(red(n5, n6)), introduced(assumption)).
% 0.22/0.50 tff(666,plain,
% 0.22/0.50 (~red(n1, n6)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[586, 109, 11, 665, 95])).
% 0.22/0.50 tff(667,plain,
% 0.22/0.50 (green(n1, n6)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[300, 666])).
% 0.22/0.50 tff(668,plain,
% 0.22/0.50 (~red(n3, n6)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[630, 109, 11, 665, 2])).
% 0.22/0.50 tff(669,plain,
% 0.22/0.50 (green(n3, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[195, 668])).
% 0.22/0.51 tff(670,plain,
% 0.22/0.51 (~red(n1, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[253, 95, 2])).
% 0.22/0.51 tff(671,plain,
% 0.22/0.51 (green(n1, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[243, 670])).
% 0.22/0.51 tff(672,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n6)) | (~green(n1, n6)) | (~green(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n1, n6)) | (~green(n1, n3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(673,plain,
% 0.22/0.51 ((goal | (~green(n1, n3)) | (~green(n3, n6)) | (~green(n1, n6))) <=> (goal | (~green(n3, n6)) | (~green(n1, n6)) | (~green(n1, n3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(674,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n6)) | (~green(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n6)) | (~green(n1, n6)) | (~green(n1, n3))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[673])).
% 0.22/0.51 tff(675,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n6)) | (~green(n1, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n1, n6)) | (~green(n1, n3)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[674, 672])).
% 0.22/0.51 tff(676,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n1, n3)) | (~green(n3, n6)) | (~green(n1, n6)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(677,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n1, n6)) | (~green(n1, n3))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.22/0.51 tff(678,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[677, 24, 11, 671, 669, 667])).
% 0.22/0.51 tff(679,plain,((~red(n5, n6)) | (~red(n1, n5)) | (~red(n3, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(680,plain,
% 0.22/0.51 (~red(n5, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[679, 664, 2])).
% 0.22/0.51 tff(681,plain,
% 0.22/0.51 (green(n5, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[567, 680])).
% 0.22/0.51 tff(682,plain,
% 0.22/0.51 (~green(n2, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[479, 681, 3])).
% 0.22/0.51 tff(683,plain,
% 0.22/0.51 (red(n2, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[469, 682])).
% 0.22/0.51 tff(684,plain,
% 0.22/0.51 (~red(n4, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[166, 683, 650])).
% 0.22/0.51 tff(685,plain,
% 0.22/0.51 (green(n4, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[155, 684])).
% 0.22/0.51 tff(686,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n4, n6)) | (~green(n5, n6)) | (~green(n4, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n4, n6)) | (~green(n5, n6)) | (~green(n4, n5)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(687,plain,
% 0.22/0.51 ((goal | (~green(n4, n5)) | (~green(n5, n6)) | (~green(n4, n6))) <=> (goal | (~green(n4, n6)) | (~green(n5, n6)) | (~green(n4, n5)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(688,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n4, n5)) | (~green(n5, n6)) | (~green(n4, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n4, n6)) | (~green(n5, n6)) | (~green(n4, n5))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[687])).
% 0.22/0.51 tff(689,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n4, n5)) | (~green(n5, n6)) | (~green(n4, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n4, n6)) | (~green(n5, n6)) | (~green(n4, n5)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[688, 686])).
% 0.22/0.51 tff(690,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n4, n5)) | (~green(n5, n6)) | (~green(n4, n6)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(691,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n4, n6)) | (~green(n5, n6)) | (~green(n4, n5))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.22/0.51 tff(692,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[691, 24, 11, 640, 681, 685])).
% 0.22/0.51 tff(693,plain,((~green(n2, n5)) | (~red(n3, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(694,plain,
% 0.22/0.51 (~green(n2, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[693, 2])).
% 0.22/0.51 tff(695,plain,
% 0.22/0.51 (red(n2, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[442, 694])).
% 0.22/0.51 tff(696,plain,
% 0.22/0.51 (~red(n2, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[501, 695, 2])).
% 0.22/0.51 tff(697,plain,
% 0.22/0.51 (green(n2, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[279, 696])).
% 0.22/0.51 tff(698,plain,
% 0.22/0.51 (~red(n1, n2)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[430, 95, 695])).
% 0.22/0.51 tff(699,plain,
% 0.22/0.51 (green(n1, n2)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[350, 698])).
% 0.22/0.51 tff(700,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[403, 699, 671, 697])).
% 0.22/0.51 tff(701,plain,((~red(n1, n5)) | (~red(n3, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(702,plain,
% 0.22/0.51 (~red(n1, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[701, 2])).
% 0.22/0.51 tff(703,plain,
% 0.22/0.51 (green(n1, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[93, 702])).
% 0.22/0.51 tff(704,plain,
% 0.22/0.51 (~red(n2, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[597, 109, 11, 665, 695])).
% 0.22/0.51 tff(705,plain,
% 0.22/0.51 (green(n2, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[469, 704])).
% 0.22/0.51 tff(706,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n6)) | (~green(n2, n6)) | (~green(n2, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n2, n6)) | (~green(n2, n3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(707,plain,
% 0.22/0.51 ((goal | (~green(n2, n3)) | (~green(n3, n6)) | (~green(n2, n6))) <=> (goal | (~green(n3, n6)) | (~green(n2, n6)) | (~green(n2, n3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(708,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n6)) | (~green(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n6)) | (~green(n2, n6)) | (~green(n2, n3))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[707])).
% 0.22/0.51 tff(709,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n6)) | (~green(n2, n6)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n2, n6)) | (~green(n2, n3)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[708, 706])).
% 0.22/0.51 tff(710,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n2, n3)) | (~green(n3, n6)) | (~green(n2, n6)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(711,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n6)) | (~green(n2, n6)) | (~green(n2, n3))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.22/0.51 tff(712,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[711, 24, 11, 395, 471, 256])).
% 0.22/0.51 tff(713,plain,((~green(n2, n3)) | (~green(n2, n6)) | (~green(n3, n6))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(714,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[713, 705, 669, 697])).
% 0.22/0.51 tff(715,plain,((~red(n5, n6)) | (~red(n3, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(716,plain,
% 0.22/0.51 (~red(n5, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[715, 2])).
% 0.22/0.51 tff(717,plain,
% 0.22/0.51 (green(n5, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[567, 716])).
% 0.22/0.51 tff(718,plain,
% 0.22/0.51 (~green(n1, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[32, 717, 703])).
% 0.22/0.51 tff(719,plain,
% 0.22/0.51 (red(n1, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[300, 718])).
% 0.22/0.51 tff(720,plain,
% 0.22/0.51 (~green(n4, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[691, 24, 11, 640, 717])).
% 0.22/0.51 tff(721,plain,
% 0.22/0.51 (red(n4, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[155, 720])).
% 0.22/0.51 tff(722,plain,
% 0.22/0.51 (~red(n1, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[329, 721, 719])).
% 0.22/0.51 tff(723,plain,
% 0.22/0.51 (green(n1, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[126, 722])).
% 0.22/0.51 tff(724,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[660, 24, 11, 640, 723, 703])).
% 0.22/0.51 tff(725,plain,(~red(n3, n5)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(726,plain,
% 0.22/0.51 (green(n3, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[210, 725])).
% 0.22/0.51 tff(727,plain,
% 0.22/0.51 ((~green(n5, n6)) | (~green(n3, n6))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[259, 726])).
% 0.22/0.51 tff(728,plain,
% 0.22/0.51 (~green(n3, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[727, 1])).
% 0.22/0.51 tff(729,plain,
% 0.22/0.51 (red(n3, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[195, 728])).
% 0.22/0.51 tff(730,plain,
% 0.22/0.51 (~green(n4, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[691, 24, 11, 640, 1])).
% 0.22/0.51 tff(731,plain,
% 0.22/0.51 (red(n4, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[155, 730])).
% 0.22/0.51 tff(732,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n3, n5)) | (~green(n4, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n3, n5)) | (~green(n4, n5)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(733,plain,
% 0.22/0.51 ((goal | (~green(n3, n4)) | (~green(n4, n5)) | (~green(n3, n5))) <=> (goal | (~green(n3, n4)) | (~green(n3, n5)) | (~green(n4, n5)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(734,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n4, n5)) | (~green(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n3, n5)) | (~green(n4, n5))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[733])).
% 0.22/0.51 tff(735,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n4, n5)) | (~green(n3, n5)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n3, n5)) | (~green(n4, n5)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[734, 732])).
% 0.22/0.51 tff(736,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | (goal | (~green(n3, n4)) | (~green(n4, n5)) | (~green(n3, n5)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(737,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~green(A, B)) | (~green(B, C)) | (~green(A, C)))) | goal | (~green(n3, n4)) | (~green(n3, n5)) | (~green(n4, n5))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.22/0.51 tff(738,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[737, 24, 11, 230, 640, 726])).
% 0.22/0.51 tff(739,plain,(~green(n3, n4)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(740,plain,
% 0.22/0.51 (red(n3, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[227, 739])).
% 0.22/0.51 tff(741,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[183, 109, 11, 740, 731, 729])).
% 0.22/0.51 tff(742,plain,(~green(n5, n6)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(743,plain,
% 0.22/0.51 (red(n5, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[567, 742])).
% 0.22/0.51 tff(744,plain,
% 0.22/0.51 (~red(n1, n2)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[430, 422, 95])).
% 0.22/0.51 tff(745,plain,
% 0.22/0.51 (green(n1, n2)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[350, 744])).
% 0.22/0.51 tff(746,plain,
% 0.22/0.51 (~green(n2, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[555, 745, 667])).
% 0.22/0.51 tff(747,plain,
% 0.22/0.51 (red(n2, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[469, 746])).
% 0.22/0.51 tff(748,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[597, 109, 11, 665, 422, 747])).
% 0.22/0.51 tff(749,plain,((~red(n2, n5)) | (~red(n5, n6)) | (~red(n1, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(750,plain,
% 0.22/0.51 (~red(n2, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[749, 665, 95])).
% 0.22/0.51 tff(751,plain,
% 0.22/0.51 (green(n2, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[442, 750])).
% 0.22/0.51 tff(752,plain,
% 0.22/0.51 (~green(n2, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[648, 751])).
% 0.22/0.51 tff(753,plain,
% 0.22/0.51 (red(n2, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[178, 752])).
% 0.22/0.51 tff(754,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[531, 109, 11, 263, 740, 158])).
% 0.22/0.51 tff(755,plain,((~red(n2, n3)) | (~red(n2, n4))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(756,plain,
% 0.22/0.51 (~red(n2, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[755, 753])).
% 0.22/0.51 tff(757,plain,
% 0.22/0.51 (green(n2, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[279, 756])).
% 0.22/0.51 tff(758,plain,
% 0.22/0.51 ((~green(n2, n3)) | (~green(n1, n3))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[523, 726])).
% 0.22/0.51 tff(759,plain,
% 0.22/0.51 (~green(n1, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[758, 757])).
% 0.22/0.51 tff(760,plain,
% 0.22/0.51 (red(n1, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[243, 759])).
% 0.22/0.51 tff(761,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n4)) | (~red(n3, n4)) | (~red(n1, n3)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n4)) | (~red(n3, n4)) | (~red(n1, n3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(762,plain,
% 0.22/0.51 ((goal | (~red(n1, n3)) | (~red(n3, n4)) | (~red(n1, n4))) <=> (goal | (~red(n1, n4)) | (~red(n3, n4)) | (~red(n1, n3)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(763,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n4)) | (~red(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n4)) | (~red(n3, n4)) | (~red(n1, n3))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[762])).
% 0.22/0.51 tff(764,plain,
% 0.22/0.51 (((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n4)) | (~red(n1, n4)))) <=> ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n4)) | (~red(n3, n4)) | (~red(n1, n3)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[763, 761])).
% 0.22/0.51 tff(765,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | (goal | (~red(n1, n3)) | (~red(n3, n4)) | (~red(n1, n4)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(766,plain,
% 0.22/0.51 ((~![A: $i, B: $i, C: $i] : (goal | (~red(A, B)) | (~red(B, C)) | (~red(A, C)))) | goal | (~red(n1, n4)) | (~red(n3, n4)) | (~red(n1, n3))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.22/0.51 tff(767,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[766, 109, 11, 740, 245, 96])).
% 0.22/0.51 tff(768,plain,((~red(n1, n3)) | (~red(n1, n4))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(769,plain,
% 0.22/0.51 (~red(n1, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[768, 760])).
% 0.22/0.51 tff(770,plain,
% 0.22/0.51 (green(n1, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[126, 769])).
% 0.22/0.51 tff(771,plain,
% 0.22/0.51 (~green(n4, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[137, 770, 667])).
% 0.22/0.51 tff(772,plain,
% 0.22/0.51 (red(n4, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[155, 771])).
% 0.22/0.51 tff(773,plain,
% 0.22/0.51 (~red(n2, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[166, 772, 753])).
% 0.22/0.51 tff(774,plain,
% 0.22/0.51 (green(n2, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[469, 773])).
% 0.22/0.51 tff(775,plain,
% 0.22/0.51 (~green(n3, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[713, 774, 757])).
% 0.22/0.51 tff(776,plain,
% 0.22/0.51 (red(n3, n6)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[195, 775])).
% 0.22/0.51 tff(777,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[183, 109, 11, 740, 772, 776])).
% 0.22/0.51 tff(778,plain,((~red(n5, n6)) | (~red(n1, n5))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(779,plain,
% 0.22/0.51 (~red(n1, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[778, 743])).
% 0.22/0.51 tff(780,plain,
% 0.22/0.51 (green(n1, n5)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[93, 779])).
% 0.22/0.51 tff(781,plain,
% 0.22/0.51 ((~green(n1, n3)) | (~green(n1, n5))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[384, 726])).
% 0.22/0.51 tff(782,plain,
% 0.22/0.51 (~green(n1, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[781, 780])).
% 0.22/0.51 tff(783,plain,
% 0.22/0.51 (red(n1, n3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[243, 782])).
% 0.22/0.51 tff(784,plain,
% 0.22/0.51 (~red(n1, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[768, 783])).
% 0.22/0.51 tff(785,plain,
% 0.22/0.51 (green(n1, n4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[126, 784])).
% 0.22/0.51 tff(786,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[660, 24, 11, 640, 785, 780])).
% 0.22/0.51 % SZS output end Proof
% 0.22/0.51 % E exiting
%------------------------------------------------------------------------------