%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU266+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:27:26 AM UTC 2025
% Result : Theorem 2.56s 2.72s
% Output : Proof 2.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU266+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 06:36:20 EDT 2025
% 0.14/0.35 % CPUTime :
% 2.56/2.72 % SZS status Theorem
% 2.56/2.72 % SZS output start Proof
% 2.56/2.72 tff(in_type, type, (
% 2.56/2.72 in: ( $i * $i ) > $o)).
% 2.56/2.72 tff(relation_rng_type, type, (
% 2.56/2.72 relation_rng: $i > $i)).
% 2.56/2.72 tff(tptp_fun_C_8_type, type, (
% 2.56/2.72 tptp_fun_C_8: $i)).
% 2.56/2.72 tff(tptp_fun_C_1_type, type, (
% 2.56/2.72 tptp_fun_C_1: ( $i * $i ) > $i)).
% 2.56/2.72 tff(tptp_fun_B_9_type, type, (
% 2.56/2.72 tptp_fun_B_9: $i)).
% 2.56/2.72 tff(relation_dom_type, type, (
% 2.56/2.72 relation_dom: $i > $i)).
% 2.56/2.72 tff(tptp_fun_D_2_type, type, (
% 2.56/2.72 tptp_fun_D_2: ( $i * $i ) > $i)).
% 2.56/2.72 tff(ordered_pair_type, type, (
% 2.56/2.72 ordered_pair: ( $i * $i ) > $i)).
% 2.56/2.72 tff(tptp_fun_E_11_type, type, (
% 2.56/2.72 tptp_fun_E_11: $i > $i)).
% 2.56/2.72 tff(relation_rng_as_subset_type, type, (
% 2.56/2.72 relation_rng_as_subset: ( $i * $i * $i ) > $i)).
% 2.56/2.72 tff(tptp_fun_A_10_type, type, (
% 2.56/2.72 tptp_fun_A_10: $i)).
% 2.56/2.72 tff(relation_of2_type, type, (
% 2.56/2.72 relation_of2: ( $i * $i * $i ) > $o)).
% 2.56/2.72 tff(relation_of2_as_subset_type, type, (
% 2.56/2.72 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 2.56/2.72 tff(tptp_fun_D_12_type, type, (
% 2.56/2.72 tptp_fun_D_12: $i)).
% 2.56/2.72 tff(tptp_fun_D_0_type, type, (
% 2.56/2.72 tptp_fun_D_0: ( $i * $i ) > $i)).
% 2.56/2.72 tff(relation_type, type, (
% 2.56/2.72 relation: $i > $o)).
% 2.56/2.72 tff(element_type, type, (
% 2.56/2.72 element: ( $i * $i ) > $o)).
% 2.56/2.72 tff(powerset_type, type, (
% 2.56/2.72 powerset: $i > $i)).
% 2.56/2.72 tff(cartesian_product2_type, type, (
% 2.56/2.72 cartesian_product2: ( $i * $i ) > $i)).
% 2.56/2.72 tff(empty_type, type, (
% 2.56/2.72 empty: $i > $o)).
% 2.56/2.72 tff(1,assumption,(in(tptp_fun_C_1(B!9, C!8), B!9)), introduced(assumption)).
% 2.56/2.72 tff(2,plain,
% 2.56/2.72 ((B!9 = relation_rng_as_subset(A!10, B!9, C!8)) <=> (relation_rng_as_subset(A!10, B!9, C!8) = B!9)),
% 2.56/2.72 inference(commutativity,[status(thm)],[])).
% 2.56/2.72 tff(3,plain,
% 2.56/2.72 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 2.56/2.72 inference(bind,[status(th)],[])).
% 2.56/2.72 tff(4,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 2.56/2.72 inference(quant_intro,[status(thm)],[3])).
% 2.56/2.72 tff(5,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 2.56/2.72 inference(rewrite,[status(thm)],[])).
% 2.56/2.72 tff(6,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 2.56/2.72 tff(7,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.56/2.72 tff(8,plain,(
% 2.56/2.72 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 2.56/2.72 inference(skolemize,[status(sab)],[7])).
% 2.56/2.72 tff(9,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[8, 4])).
% 2.56/2.72 tff(10,plain,
% 2.56/2.72 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(C!8, A!10, B!9) <=> relation_of2(C!8, A!10, B!9))),
% 2.56/2.72 inference(quant_inst,[status(thm)],[])).
% 2.56/2.72 tff(11,plain,
% 2.56/2.72 (relation_of2_as_subset(C!8, A!10, B!9) <=> relation_of2(C!8, A!10, B!9)),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[10, 9])).
% 2.56/2.72 tff(12,plain,
% 2.56/2.72 ((relation_of2_as_subset(C!8, A!10, B!9) & (((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))))) <=> (relation_of2_as_subset(C!8, A!10, B!9) & ((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))))),
% 2.56/2.72 inference(rewrite,[status(thm)],[])).
% 2.56/2.72 tff(13,plain,
% 2.56/2.72 (((![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8)) | (relation_rng_as_subset(A!10, B!9, C!8) = B!9)) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)))) <=> (((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))))),
% 2.56/2.72 inference(rewrite,[status(thm)],[])).
% 2.56/2.72 tff(14,plain,
% 2.56/2.72 ((relation_of2_as_subset(C!8, A!10, B!9) & ((![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8)) | (relation_rng_as_subset(A!10, B!9, C!8) = B!9)) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))))) <=> (relation_of2_as_subset(C!8, A!10, B!9) & (((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)))))),
% 2.56/2.72 inference(monotonicity,[status(thm)],[13])).
% 2.56/2.72 tff(15,plain,
% 2.56/2.72 ((relation_of2_as_subset(C!8, A!10, B!9) & ((![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8)) | (relation_rng_as_subset(A!10, B!9, C!8) = B!9)) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))))) <=> (relation_of2_as_subset(C!8, A!10, B!9) & ((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))))),
% 2.56/2.72 inference(transitivity,[status(thm)],[14, 12])).
% 2.56/2.72 tff(16,plain,
% 2.56/2.72 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B)))) <=> (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B))))),
% 2.56/2.72 inference(rewrite,[status(thm)],[])).
% 2.56/2.72 tff(17,plain,
% 2.56/2.72 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B)))) <=> (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B))))),
% 2.56/2.72 inference(rewrite,[status(thm)],[])).
% 2.56/2.72 tff(18,axiom,(~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_relset_1')).
% 2.56/2.72 tff(19,plain,
% 2.56/2.72 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B)))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[18, 17])).
% 2.56/2.72 tff(20,plain,
% 2.56/2.72 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B)))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[19, 16])).
% 2.56/2.72 tff(21,plain,
% 2.56/2.72 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B)))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[20, 16])).
% 2.56/2.72 tff(22,plain,
% 2.56/2.72 (~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (![D: $i] : (~(in(D, B) & ![E: $i] : (~in(ordered_pair(E, D), C)))) <=> (relation_rng_as_subset(A, B, C) = B)))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[21, 16])).
% 2.56/2.72 tff(23,plain,
% 2.56/2.72 (relation_of2_as_subset(C!8, A!10, B!9) & ((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) & ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[22, 15])).
% 2.56/2.72 tff(24,plain,
% 2.56/2.72 (relation_of2_as_subset(C!8, A!10, B!9)),
% 2.56/2.72 inference(and_elim,[status(thm)],[23])).
% 2.56/2.72 tff(25,plain,
% 2.56/2.72 ((~(relation_of2_as_subset(C!8, A!10, B!9) <=> relation_of2(C!8, A!10, B!9))) | (~relation_of2_as_subset(C!8, A!10, B!9)) | relation_of2(C!8, A!10, B!9)),
% 2.56/2.72 inference(tautology,[status(thm)],[])).
% 2.56/2.72 tff(26,plain,
% 2.56/2.72 ((~(relation_of2_as_subset(C!8, A!10, B!9) <=> relation_of2(C!8, A!10, B!9))) | relation_of2(C!8, A!10, B!9)),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[25, 24])).
% 2.56/2.72 tff(27,plain,
% 2.56/2.72 (relation_of2(C!8, A!10, B!9)),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[26, 11])).
% 2.56/2.72 tff(28,plain,
% 2.56/2.72 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C))) <=> ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C))))),
% 2.56/2.72 inference(bind,[status(th)],[])).
% 2.56/2.72 tff(29,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))),
% 2.56/2.72 inference(quant_intro,[status(thm)],[28])).
% 2.56/2.72 tff(30,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))),
% 2.56/2.72 inference(rewrite,[status(thm)],[])).
% 2.56/2.72 tff(31,plain,
% 2.56/2.72 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2(C, A, B) => (relation_rng_as_subset(A, B, C) = relation_rng(C))) <=> ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C))))),
% 2.56/2.72 inference(bind,[status(th)],[])).
% 2.56/2.72 tff(32,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => (relation_rng_as_subset(A, B, C) = relation_rng(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))),
% 2.56/2.72 inference(quant_intro,[status(thm)],[31])).
% 2.56/2.72 tff(33,axiom,(![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => (relation_rng_as_subset(A, B, C) = relation_rng(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k5_relset_1')).
% 2.56/2.72 tff(34,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[33, 32])).
% 2.56/2.72 tff(35,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[34, 30])).
% 2.56/2.72 tff(36,plain,(
% 2.56/2.72 ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))),
% 2.56/2.72 inference(skolemize,[status(sab)],[35])).
% 2.56/2.72 tff(37,plain,
% 2.56/2.72 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[36, 29])).
% 2.56/2.72 tff(38,plain,
% 2.56/2.72 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))) | ((~relation_of2(C!8, A!10, B!9)) | (relation_rng_as_subset(A!10, B!9, C!8) = relation_rng(C!8)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))) | (~relation_of2(C!8, A!10, B!9)) | (relation_rng_as_subset(A!10, B!9, C!8) = relation_rng(C!8)))),
% 2.56/2.72 inference(rewrite,[status(thm)],[])).
% 2.56/2.72 tff(39,plain,
% 2.56/2.72 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))) | ((~relation_of2(C!8, A!10, B!9)) | (relation_rng_as_subset(A!10, B!9, C!8) = relation_rng(C!8)))),
% 2.56/2.72 inference(quant_inst,[status(thm)],[])).
% 2.56/2.72 tff(40,plain,
% 2.56/2.72 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_rng_as_subset(A, B, C) = relation_rng(C)))) | (~relation_of2(C!8, A!10, B!9)) | (relation_rng_as_subset(A!10, B!9, C!8) = relation_rng(C!8))),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[39, 38])).
% 2.56/2.72 tff(41,plain,
% 2.56/2.72 (relation_rng_as_subset(A!10, B!9, C!8) = relation_rng(C!8)),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 2.56/2.73 tff(42,plain,
% 2.56/2.73 (relation_rng(C!8) = relation_rng_as_subset(A!10, B!9, C!8)),
% 2.56/2.73 inference(symmetry,[status(thm)],[41])).
% 2.56/2.73 tff(43,plain,
% 2.56/2.73 ((B!9 = relation_rng(C!8)) <=> (B!9 = relation_rng_as_subset(A!10, B!9, C!8))),
% 2.56/2.73 inference(monotonicity,[status(thm)],[42])).
% 2.56/2.73 tff(44,plain,
% 2.56/2.73 ((B!9 = relation_rng(C!8)) <=> (relation_rng_as_subset(A!10, B!9, C!8) = B!9)),
% 2.56/2.73 inference(transitivity,[status(thm)],[43, 2])).
% 2.56/2.73 tff(45,plain,
% 2.56/2.73 ((relation_rng_as_subset(A!10, B!9, C!8) = B!9) <=> (B!9 = relation_rng(C!8))),
% 2.56/2.73 inference(symmetry,[status(thm)],[44])).
% 2.56/2.73 tff(46,plain,
% 2.56/2.73 ((~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)) <=> (~(B!9 = relation_rng(C!8)))),
% 2.56/2.73 inference(monotonicity,[status(thm)],[45])).
% 2.56/2.73 tff(47,assumption,(~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8))))), introduced(assumption)).
% 2.56/2.73 tff(48,plain,
% 2.56/2.73 (((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8)))) | in(D!12, B!9)),
% 2.56/2.73 inference(tautology,[status(thm)],[])).
% 2.56/2.73 tff(49,plain,
% 2.56/2.73 (in(D!12, B!9)),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[48, 47])).
% 2.56/2.73 tff(50,plain,
% 2.56/2.73 (((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8)))) | ![E: $i] : (~in(ordered_pair(E, D!12), C!8))),
% 2.56/2.73 inference(tautology,[status(thm)],[])).
% 2.56/2.73 tff(51,plain,
% 2.56/2.73 (![E: $i] : (~in(ordered_pair(E, D!12), C!8))),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[50, 47])).
% 2.56/2.73 tff(52,assumption,(in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8)), introduced(assumption)).
% 2.56/2.73 tff(53,assumption,(![E: $i] : (~in(ordered_pair(E, D!12), C!8))), introduced(assumption)).
% 2.56/2.73 tff(54,plain,
% 2.56/2.73 ((~![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8))),
% 2.56/2.73 inference(quant_inst,[status(thm)],[])).
% 2.56/2.73 tff(55,plain,
% 2.56/2.73 ($false),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[54, 53, 52])).
% 2.56/2.73 tff(56,plain,((~in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8)))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.73 tff(57,plain,
% 2.56/2.73 (~in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8)),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[56, 51])).
% 2.56/2.73 tff(58,assumption,(relation_rng_as_subset(A!10, B!9, C!8) = B!9), introduced(assumption)).
% 2.56/2.73 tff(59,plain,
% 2.56/2.73 (relation_rng(C!8) = B!9),
% 2.56/2.73 inference(transitivity,[status(thm)],[42, 58])).
% 2.56/2.73 tff(60,plain,
% 2.56/2.73 (in(D!12, relation_rng(C!8)) <=> in(D!12, B!9)),
% 2.56/2.73 inference(monotonicity,[status(thm)],[59])).
% 2.56/2.73 tff(61,plain,
% 2.56/2.73 (in(D!12, B!9) <=> in(D!12, relation_rng(C!8))),
% 2.56/2.73 inference(symmetry,[status(thm)],[60])).
% 2.56/2.73 tff(62,assumption,(in(D!12, B!9)), introduced(assumption)).
% 2.56/2.73 tff(63,plain,
% 2.56/2.73 (in(D!12, relation_rng(C!8))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[62, 61])).
% 2.56/2.73 tff(64,plain,
% 2.56/2.73 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(65,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[64])).
% 2.56/2.73 tff(66,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(67,plain,
% 2.56/2.73 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(68,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[67])).
% 2.56/2.73 tff(69,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 2.56/2.73 tff(70,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[69, 68])).
% 2.56/2.73 tff(71,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[70, 66])).
% 2.56/2.73 tff(72,plain,(
% 2.56/2.73 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 2.56/2.73 inference(skolemize,[status(sab)],[71])).
% 2.56/2.73 tff(73,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[72, 65])).
% 2.56/2.73 tff(74,plain,
% 2.56/2.73 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(C!8, A!10, B!9)) | element(C!8, powerset(cartesian_product2(A!10, B!9))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(C!8, A!10, B!9)) | element(C!8, powerset(cartesian_product2(A!10, B!9))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(75,plain,
% 2.56/2.73 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(C!8, A!10, B!9)) | element(C!8, powerset(cartesian_product2(A!10, B!9))))),
% 2.56/2.73 inference(quant_inst,[status(thm)],[])).
% 2.56/2.73 tff(76,plain,
% 2.56/2.73 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(C!8, A!10, B!9)) | element(C!8, powerset(cartesian_product2(A!10, B!9)))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.56/2.73 tff(77,plain,
% 2.56/2.73 (element(C!8, powerset(cartesian_product2(A!10, B!9)))),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[76, 73, 24])).
% 2.56/2.73 tff(78,plain,
% 2.56/2.73 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(79,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[78])).
% 2.56/2.73 tff(80,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(81,plain,
% 2.56/2.73 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(82,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[81])).
% 2.56/2.73 tff(83,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 2.56/2.73 tff(84,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.56/2.73 tff(85,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[84, 80])).
% 2.56/2.73 tff(86,plain,(
% 2.56/2.73 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(skolemize,[status(sab)],[85])).
% 2.56/2.73 tff(87,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[86, 79])).
% 2.56/2.73 tff(88,plain,
% 2.56/2.73 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(C!8) | (~element(C!8, powerset(cartesian_product2(A!10, B!9)))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(C!8) | (~element(C!8, powerset(cartesian_product2(A!10, B!9)))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(89,plain,
% 2.56/2.73 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(C!8) | (~element(C!8, powerset(cartesian_product2(A!10, B!9)))))),
% 2.56/2.73 inference(quant_inst,[status(thm)],[])).
% 2.56/2.73 tff(90,plain,
% 2.56/2.73 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(C!8) | (~element(C!8, powerset(cartesian_product2(A!10, B!9))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[89, 88])).
% 2.56/2.73 tff(91,plain,
% 2.56/2.73 (relation(C!8)),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[90, 87, 77])).
% 2.56/2.73 tff(92,plain,
% 2.56/2.73 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))))))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(93,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[92])).
% 2.56/2.73 tff(94,plain,
% 2.56/2.73 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))))))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(95,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[94])).
% 2.56/2.73 tff(96,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))),
% 2.56/2.73 inference(transitivity,[status(thm)],[95, 93])).
% 2.56/2.73 tff(97,plain,
% 2.56/2.73 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))))))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(98,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[97])).
% 2.56/2.73 tff(99,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(100,plain,
% 2.56/2.73 (^[A: $i] : rewrite((relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(101,plain,
% 2.56/2.73 (![A: $i] : (relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[100])).
% 2.56/2.73 tff(102,axiom,(![A: $i] : (relation(A) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_relat_1')).
% 2.56/2.73 tff(103,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[102, 101])).
% 2.56/2.73 tff(104,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : in(ordered_pair(D, C), A))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[103, 99])).
% 2.56/2.73 tff(105,plain,(
% 2.56/2.73 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A)) & (in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A)) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))),
% 2.56/2.73 inference(skolemize,[status(sab)],[104])).
% 2.56/2.73 tff(106,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[105, 98])).
% 2.56/2.73 tff(107,plain,
% 2.56/2.73 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[106, 96])).
% 2.56/2.73 tff(108,plain,
% 2.56/2.73 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))) | (~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8)))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(109,plain,
% 2.56/2.73 (((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((B = relation_rng(C!8)) | (~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8))))))))))) <=> ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8)))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(110,plain,
% 2.56/2.73 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((B = relation_rng(C!8)) | (~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))))),
% 2.56/2.73 inference(monotonicity,[status(thm)],[109])).
% 2.56/2.73 tff(111,plain,
% 2.56/2.73 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((B = relation_rng(C!8)) | (~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))) | (~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8)))))))),
% 2.56/2.73 inference(transitivity,[status(thm)],[110, 108])).
% 2.56/2.73 tff(112,plain,
% 2.56/2.73 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))) | ((~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((B = relation_rng(C!8)) | (~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))))))))),
% 2.56/2.73 inference(quant_inst,[status(thm)],[])).
% 2.56/2.73 tff(113,plain,
% 2.56/2.73 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, A), C), A))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), A)))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_1(B, A)), A))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, A)), A)))))))))))) | (~relation(C!8)) | ![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.56/2.73 tff(114,plain,
% 2.56/2.73 (![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[113, 107, 91])).
% 2.56/2.73 tff(115,plain,
% 2.56/2.73 (((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(116,plain,
% 2.56/2.73 ((~(~![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(117,plain,
% 2.56/2.73 (((~![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))) | $false) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(118,plain,
% 2.56/2.73 ((~$true) <=> $false),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(119,plain,
% 2.56/2.73 (((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | $true) <=> $true),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(120,plain,
% 2.56/2.73 ((relation_rng(C!8) = relation_rng(C!8)) <=> $true),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(121,plain,
% 2.56/2.73 (((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) <=> ((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(122,plain,
% 2.56/2.73 ((~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))) <=> (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))))),
% 2.56/2.73 inference(monotonicity,[status(thm)],[121])).
% 2.56/2.73 tff(123,plain,
% 2.56/2.73 (((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))))) <=> ((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))),
% 2.56/2.73 inference(monotonicity,[status(thm)],[122])).
% 2.56/2.73 tff(124,plain,
% 2.56/2.73 ((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) <=> (~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))))))),
% 2.56/2.73 inference(monotonicity,[status(thm)],[123])).
% 2.56/2.73 tff(125,plain,
% 2.56/2.73 (((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8))) <=> ((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | $true)),
% 2.56/2.73 inference(monotonicity,[status(thm)],[124, 120])).
% 2.56/2.73 tff(126,plain,
% 2.56/2.73 (((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8))) <=> $true),
% 2.56/2.73 inference(transitivity,[status(thm)],[125, 119])).
% 2.56/2.73 tff(127,plain,
% 2.56/2.73 ((~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8)))) <=> (~$true)),
% 2.56/2.73 inference(monotonicity,[status(thm)],[126])).
% 2.56/2.73 tff(128,plain,
% 2.56/2.73 ((~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8)))) <=> $false),
% 2.56/2.73 inference(transitivity,[status(thm)],[127, 118])).
% 2.56/2.73 tff(129,plain,
% 2.56/2.73 ((~((~(relation_rng(C!8) = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(130,plain,
% 2.56/2.73 (((~((~(relation_rng(C!8) = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8))))) <=> ((~![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))) | $false)),
% 2.56/2.74 inference(monotonicity,[status(thm)],[129, 128])).
% 2.56/2.74 tff(131,plain,
% 2.56/2.74 (((~((~(relation_rng(C!8) = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8))))) <=> (~![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))),
% 2.56/2.74 inference(transitivity,[status(thm)],[130, 117])).
% 2.56/2.74 tff(132,plain,
% 2.56/2.74 ((~((~((~(relation_rng(C!8) = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8)))))) <=> (~(~![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))))),
% 2.56/2.74 inference(monotonicity,[status(thm)],[131])).
% 2.56/2.74 tff(133,plain,
% 2.56/2.74 ((~((~((~(relation_rng(C!8) = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8)))))) <=> ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))),
% 2.56/2.74 inference(transitivity,[status(thm)],[132, 116])).
% 2.56/2.74 tff(134,plain,
% 2.56/2.74 (((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | (~((~((~(relation_rng(C!8) = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))),
% 2.56/2.74 inference(monotonicity,[status(thm)],[133])).
% 2.56/2.74 tff(135,plain,
% 2.56/2.74 (((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | (~((~((~(relation_rng(C!8) = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8))))))) <=> ((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))),
% 2.56/2.74 inference(transitivity,[status(thm)],[134, 115])).
% 2.56/2.74 tff(136,plain,
% 2.56/2.74 ((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | (~((~((~(relation_rng(C!8) = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8)) | in(ordered_pair(tptp_fun_D_2(relation_rng(C!8), C!8), tptp_fun_C_1(relation_rng(C!8), C!8)), C!8))) | (~((~in(tptp_fun_C_1(relation_rng(C!8), C!8), relation_rng(C!8))) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(relation_rng(C!8), C!8)), C!8)))))) | (relation_rng(C!8) = relation_rng(C!8))))))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(137,plain,
% 2.56/2.74 ((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | ![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[136, 135])).
% 2.56/2.74 tff(138,plain,
% 2.56/2.74 (![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[137, 114])).
% 2.56/2.74 tff(139,plain,
% 2.56/2.74 ((~![C: $i] : (~((~((~in(C, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, C), C!8))))))) | (~((~((~in(D!12, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8))) | (~(in(D!12, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, D!12), C!8))))))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(140,plain,
% 2.56/2.74 (~((~((~in(D!12, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8))) | (~(in(D!12, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, D!12), C!8)))))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[139, 138])).
% 2.56/2.74 tff(141,plain,
% 2.56/2.74 (((~((~in(D!12, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8))) | (~(in(D!12, relation_rng(C!8)) | ![D: $i] : (~in(ordered_pair(D, D!12), C!8))))) | ((~in(D!12, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(142,plain,
% 2.56/2.74 ((~in(D!12, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[141, 140])).
% 2.56/2.74 tff(143,assumption,(~in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8)), introduced(assumption)).
% 2.56/2.74 tff(144,plain,
% 2.56/2.74 ((~((~in(D!12, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8))) | (~in(D!12, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8)),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(145,plain,
% 2.56/2.74 ((~((~in(D!12, relation_rng(C!8))) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8))) | (~in(D!12, relation_rng(C!8)))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[144, 143])).
% 2.56/2.74 tff(146,plain,
% 2.56/2.74 (~in(D!12, relation_rng(C!8))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[145, 142])).
% 2.56/2.74 tff(147,plain,
% 2.56/2.74 ($false),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[146, 63])).
% 2.56/2.74 tff(148,plain,((~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)) | (~in(D!12, B!9)) | in(ordered_pair(tptp_fun_D_0(D!12, C!8), D!12), C!8)), inference(lemma,lemma(discharge,[]))).
% 2.56/2.74 tff(149,plain,
% 2.56/2.74 (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[148, 49, 57])).
% 2.56/2.74 tff(150,plain,
% 2.56/2.74 (((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) <=> ((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(151,plain,
% 2.56/2.74 ((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))),
% 2.56/2.74 inference(and_elim,[status(thm)],[23])).
% 2.56/2.74 tff(152,plain,
% 2.56/2.74 ((relation_rng_as_subset(A!10, B!9, C!8) = B!9) | ![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[151, 150])).
% 2.56/2.74 tff(153,plain,
% 2.56/2.74 (![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[152, 149])).
% 2.56/2.74 tff(154,plain,
% 2.56/2.74 (((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) | ((~in(D!12, B!9)) | in(ordered_pair(tptp_fun_E_11(D!12), D!12), C!8))) <=> ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) | (~in(D!12, B!9)) | in(ordered_pair(tptp_fun_E_11(D!12), D!12), C!8))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(155,plain,
% 2.56/2.74 ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) | ((~in(D!12, B!9)) | in(ordered_pair(tptp_fun_E_11(D!12), D!12), C!8))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(156,plain,
% 2.56/2.74 ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) | (~in(D!12, B!9)) | in(ordered_pair(tptp_fun_E_11(D!12), D!12), C!8)),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[155, 154])).
% 2.56/2.74 tff(157,plain,
% 2.56/2.74 (in(ordered_pair(tptp_fun_E_11(D!12), D!12), C!8)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[156, 153, 49])).
% 2.56/2.74 tff(158,plain,
% 2.56/2.74 ((~![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~in(ordered_pair(tptp_fun_E_11(D!12), D!12), C!8))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(159,plain,
% 2.56/2.74 ($false),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[158, 51, 157])).
% 2.56/2.74 tff(160,plain,((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8)))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.74 tff(161,plain,
% 2.56/2.74 (((~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8)))))) <=> ((~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8))))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(162,plain,
% 2.56/2.74 (((~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8))))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))) <=> ((~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8))))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(163,plain,
% 2.56/2.74 ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) <=> (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8)))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(164,plain,
% 2.56/2.74 (((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))) <=> ((~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8))))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)))),
% 2.56/2.74 inference(monotonicity,[status(thm)],[163])).
% 2.56/2.74 tff(165,plain,
% 2.56/2.74 (((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))) <=> ((~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8))))))),
% 2.56/2.74 inference(transitivity,[status(thm)],[164, 162])).
% 2.56/2.74 tff(166,plain,
% 2.56/2.74 ((in(D!12, B!9) & ![E: $i] : (~in(ordered_pair(E, D!12), C!8))) | (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9))),
% 2.56/2.74 inference(and_elim,[status(thm)],[23])).
% 2.56/2.74 tff(167,plain,
% 2.56/2.74 ((~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8)))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[166, 165])).
% 2.56/2.74 tff(168,plain,
% 2.56/2.74 ((~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)) | (~((~in(D!12, B!9)) | (~![E: $i] : (~in(ordered_pair(E, D!12), C!8)))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[167, 161])).
% 2.56/2.74 tff(169,plain,
% 2.56/2.74 (~(relation_rng_as_subset(A!10, B!9, C!8) = B!9)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[168, 160])).
% 2.56/2.74 tff(170,plain,
% 2.56/2.74 (~(B!9 = relation_rng(C!8))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[169, 46])).
% 2.56/2.74 tff(171,plain,
% 2.56/2.74 ((~![B: $i] : (~((~((~(B = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B, C!8), B) | in(ordered_pair(tptp_fun_D_2(B, C!8), tptp_fun_C_1(B, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B, C!8), B)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B, C!8)), C!8)))))) | (B = relation_rng(C!8))))))) | (~((~((~(B!9 = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))) | (B!9 = relation_rng(C!8))))))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(172,plain,
% 2.56/2.74 (~((~((~(B!9 = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))) | (B!9 = relation_rng(C!8)))))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[171, 114])).
% 2.56/2.74 tff(173,plain,
% 2.56/2.74 (((~((~(B!9 = relation_rng(C!8))) | ![C: $i] : (~((~((~in(C, B!9)) | in(ordered_pair(tptp_fun_D_0(C, C!8), C), C!8))) | (~(in(C, B!9) | ![D: $i] : (~in(ordered_pair(D, C), C!8)))))))) | (~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))) | (B!9 = relation_rng(C!8))))) | ((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))) | (B!9 = relation_rng(C!8)))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(174,plain,
% 2.56/2.74 ((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))) | (B!9 = relation_rng(C!8))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[173, 172])).
% 2.56/2.74 tff(175,plain,
% 2.56/2.74 ((~((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))) | (B!9 = relation_rng(C!8)))) | (~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))) | (B!9 = relation_rng(C!8))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(176,plain,
% 2.56/2.74 ((~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))) | (B!9 = relation_rng(C!8))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[175, 174])).
% 2.56/2.74 tff(177,plain,
% 2.56/2.74 (~((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[176, 170])).
% 2.56/2.74 tff(178,plain,
% 2.56/2.74 (((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8))))) | ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(179,plain,
% 2.56/2.74 ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[178, 177])).
% 2.56/2.74 tff(180,plain,
% 2.56/2.74 ((~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8)))) | (~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(181,plain,
% 2.56/2.74 ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[180, 179])).
% 2.56/2.74 tff(182,plain,
% 2.56/2.74 (![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[181, 1])).
% 2.56/2.74 tff(183,plain,
% 2.56/2.74 ((~![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8))) | (~in(ordered_pair(tptp_fun_E_11(tptp_fun_C_1(B!9, C!8)), tptp_fun_C_1(B!9, C!8)), C!8))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(184,plain,
% 2.56/2.74 (~in(ordered_pair(tptp_fun_E_11(tptp_fun_C_1(B!9, C!8)), tptp_fun_C_1(B!9, C!8)), C!8)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[183, 182])).
% 2.56/2.74 tff(185,plain,
% 2.56/2.74 (![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[152, 169])).
% 2.56/2.74 tff(186,plain,
% 2.56/2.74 (((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) | ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | in(ordered_pair(tptp_fun_E_11(tptp_fun_C_1(B!9, C!8)), tptp_fun_C_1(B!9, C!8)), C!8))) <=> ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) | (~in(tptp_fun_C_1(B!9, C!8), B!9)) | in(ordered_pair(tptp_fun_E_11(tptp_fun_C_1(B!9, C!8)), tptp_fun_C_1(B!9, C!8)), C!8))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(187,plain,
% 2.56/2.74 ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) | ((~in(tptp_fun_C_1(B!9, C!8), B!9)) | in(ordered_pair(tptp_fun_E_11(tptp_fun_C_1(B!9, C!8)), tptp_fun_C_1(B!9, C!8)), C!8))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(188,plain,
% 2.56/2.74 ((~![D: $i] : ((~in(D, B!9)) | in(ordered_pair(tptp_fun_E_11(D), D), C!8))) | (~in(tptp_fun_C_1(B!9, C!8), B!9)) | in(ordered_pair(tptp_fun_E_11(tptp_fun_C_1(B!9, C!8)), tptp_fun_C_1(B!9, C!8)), C!8)),
% 2.60/2.74 inference(modus_ponens,[status(thm)],[187, 186])).
% 2.60/2.74 tff(189,plain,
% 2.60/2.74 ($false),
% 2.60/2.74 inference(unit_resolution,[status(thm)],[188, 185, 1, 184])).
% 2.60/2.74 tff(190,plain,(~in(tptp_fun_C_1(B!9, C!8), B!9)), inference(lemma,lemma(discharge,[]))).
% 2.60/2.74 tff(191,plain,
% 2.60/2.74 (((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | (~((~in(tptp_fun_C_1(B!9, C!8), B!9)) | ![D: $i] : (~in(ordered_pair(D, tptp_fun_C_1(B!9, C!8)), C!8))))) | (in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))),
% 2.60/2.74 inference(tautology,[status(thm)],[])).
% 2.60/2.74 tff(192,plain,
% 2.60/2.74 (in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8)),
% 2.60/2.74 inference(unit_resolution,[status(thm)],[191, 177])).
% 2.60/2.74 tff(193,plain,
% 2.60/2.74 ((~(in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8))) | in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8)),
% 2.60/2.74 inference(tautology,[status(thm)],[])).
% 2.60/2.74 tff(194,plain,
% 2.60/2.74 (in(tptp_fun_C_1(B!9, C!8), B!9) | in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8)),
% 2.60/2.74 inference(unit_resolution,[status(thm)],[193, 192])).
% 2.60/2.74 tff(195,plain,
% 2.60/2.74 (in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8)),
% 2.60/2.74 inference(unit_resolution,[status(thm)],[194, 190])).
% 2.60/2.74 tff(196,plain,
% 2.60/2.74 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C)))))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C)))))))),
% 2.60/2.74 inference(bind,[status(th)],[])).
% 2.60/2.74 tff(197,plain,
% 2.60/2.74 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))),
% 2.60/2.74 inference(quant_intro,[status(thm)],[196])).
% 2.60/2.74 tff(198,plain,
% 2.60/2.74 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(B, relation_rng(C))) <=> (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C)))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))), rewrite(((~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))))),
% 2.60/2.74 inference(bind,[status(th)],[])).
% 2.60/2.74 tff(199,plain,
% 2.60/2.74 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))),
% 2.60/2.74 inference(quant_intro,[status(thm)],[198])).
% 2.60/2.74 tff(200,plain,
% 2.60/2.74 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 2.60/2.74 inference(rewrite,[status(thm)],[])).
% 2.60/2.74 tff(201,plain,
% 2.60/2.74 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))) <=> ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> (relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))))), rewrite((relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))))),
% 2.60/2.74 inference(bind,[status(th)],[])).
% 2.60/2.74 tff(202,plain,
% 2.60/2.74 (![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 2.60/2.74 inference(quant_intro,[status(thm)],[201])).
% 2.60/2.74 tff(203,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_relat_1')).
% 2.60/2.75 tff(204,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[203, 202])).
% 2.60/2.75 tff(205,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[204, 200])).
% 2.60/2.75 tff(206,plain,(
% 2.60/2.75 ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 2.60/2.75 inference(skolemize,[status(sab)],[205])).
% 2.60/2.75 tff(207,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[206, 199])).
% 2.60/2.75 tff(208,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[207, 197])).
% 2.60/2.75 tff(209,plain,
% 2.60/2.75 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))) | ((~relation(C!8)) | (~in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8)) | (~((~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_D_2(B!9, C!8), relation_dom(C!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))) | (~relation(C!8)) | (~in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8)) | (~((~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_D_2(B!9, C!8), relation_dom(C!8))))))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(210,plain,
% 2.60/2.75 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))) | ((~relation(C!8)) | (~in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8)) | (~((~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_D_2(B!9, C!8), relation_dom(C!8))))))),
% 2.60/2.75 inference(quant_inst,[status(thm)],[])).
% 2.60/2.75 tff(211,plain,
% 2.60/2.75 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(B, relation_rng(C))) | (~in(A, relation_dom(C))))))) | (~relation(C!8)) | (~in(ordered_pair(tptp_fun_D_2(B!9, C!8), tptp_fun_C_1(B!9, C!8)), C!8)) | (~((~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_D_2(B!9, C!8), relation_dom(C!8)))))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[210, 209])).
% 2.60/2.75 tff(212,plain,
% 2.60/2.75 (~((~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_D_2(B!9, C!8), relation_dom(C!8))))),
% 2.60/2.75 inference(unit_resolution,[status(thm)],[211, 208, 91, 195])).
% 2.60/2.75 tff(213,plain,
% 2.60/2.75 (((~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~in(tptp_fun_D_2(B!9, C!8), relation_dom(C!8)))) | in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))),
% 2.60/2.75 inference(tautology,[status(thm)],[])).
% 2.60/2.75 tff(214,plain,
% 2.60/2.75 (in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))),
% 2.60/2.75 inference(unit_resolution,[status(thm)],[213, 212])).
% 2.60/2.75 tff(215,plain,
% 2.60/2.75 (element(relation_rng(C!8), powerset(B!9)) <=> element(relation_rng_as_subset(A!10, B!9, C!8), powerset(B!9))),
% 2.60/2.75 inference(monotonicity,[status(thm)],[42])).
% 2.60/2.75 tff(216,plain,
% 2.60/2.75 (element(relation_rng_as_subset(A!10, B!9, C!8), powerset(B!9)) <=> element(relation_rng(C!8), powerset(B!9))),
% 2.60/2.75 inference(symmetry,[status(thm)],[215])).
% 2.60/2.75 tff(217,plain,
% 2.60/2.75 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B))) <=> ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(218,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[217])).
% 2.60/2.75 tff(219,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(220,plain,
% 2.60/2.75 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2(C, A, B) => element(relation_rng_as_subset(A, B, C), powerset(B))) <=> ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(221,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => element(relation_rng_as_subset(A, B, C), powerset(B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[220])).
% 2.60/2.75 tff(222,axiom,(![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => element(relation_rng_as_subset(A, B, C), powerset(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relset_1')).
% 2.60/2.75 tff(223,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[222, 221])).
% 2.60/2.75 tff(224,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[223, 219])).
% 2.60/2.75 tff(225,plain,(
% 2.60/2.75 ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))),
% 2.60/2.75 inference(skolemize,[status(sab)],[224])).
% 2.60/2.75 tff(226,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[225, 218])).
% 2.60/2.75 tff(227,plain,
% 2.60/2.75 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))) | ((~relation_of2(C!8, A!10, B!9)) | element(relation_rng_as_subset(A!10, B!9, C!8), powerset(B!9)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))) | (~relation_of2(C!8, A!10, B!9)) | element(relation_rng_as_subset(A!10, B!9, C!8), powerset(B!9)))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(228,plain,
% 2.60/2.75 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))) | ((~relation_of2(C!8, A!10, B!9)) | element(relation_rng_as_subset(A!10, B!9, C!8), powerset(B!9)))),
% 2.60/2.75 inference(quant_inst,[status(thm)],[])).
% 2.60/2.75 tff(229,plain,
% 2.60/2.75 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | element(relation_rng_as_subset(A, B, C), powerset(B)))) | (~relation_of2(C!8, A!10, B!9)) | element(relation_rng_as_subset(A!10, B!9, C!8), powerset(B!9))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[228, 227])).
% 2.60/2.75 tff(230,plain,
% 2.60/2.75 (element(relation_rng_as_subset(A!10, B!9, C!8), powerset(B!9))),
% 2.60/2.75 inference(unit_resolution,[status(thm)],[229, 226, 27])).
% 2.60/2.75 tff(231,plain,
% 2.60/2.75 (element(relation_rng(C!8), powerset(B!9))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[230, 216])).
% 2.60/2.75 tff(232,plain,
% 2.60/2.75 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(233,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[232])).
% 2.60/2.75 tff(234,plain,
% 2.60/2.75 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(235,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[234])).
% 2.60/2.75 tff(236,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(237,plain,
% 2.60/2.75 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(238,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[237])).
% 2.60/2.75 tff(239,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 2.60/2.75 tff(240,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[239, 238])).
% 2.60/2.75 tff(241,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[240, 236])).
% 2.60/2.75 tff(242,plain,(
% 2.60/2.75 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 2.60/2.75 inference(skolemize,[status(sab)],[241])).
% 2.60/2.75 tff(243,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[242, 235])).
% 2.60/2.75 tff(244,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[243, 233])).
% 2.60/2.75 tff(245,plain,
% 2.60/2.75 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_rng(C!8), powerset(B!9))) | (~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(C!8), powerset(B!9))) | (~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(246,plain,
% 2.60/2.75 (((~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~element(relation_rng(C!8), powerset(B!9)))) <=> ((~element(relation_rng(C!8), powerset(B!9))) | (~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(247,plain,
% 2.60/2.75 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~element(relation_rng(C!8), powerset(B!9))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_rng(C!8), powerset(B!9))) | (~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8)))))),
% 2.60/2.75 inference(monotonicity,[status(thm)],[246])).
% 2.60/2.75 tff(248,plain,
% 2.60/2.75 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~element(relation_rng(C!8), powerset(B!9))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(C!8), powerset(B!9))) | (~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))))),
% 2.60/2.75 inference(transitivity,[status(thm)],[247, 245])).
% 2.60/2.75 tff(249,plain,
% 2.60/2.75 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~element(relation_rng(C!8), powerset(B!9))))),
% 2.60/2.75 inference(quant_inst,[status(thm)],[])).
% 2.60/2.75 tff(250,plain,
% 2.60/2.75 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(C!8), powerset(B!9))) | (~empty(B!9)) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[249, 248])).
% 2.60/2.75 tff(251,plain,
% 2.60/2.75 (~empty(B!9)),
% 2.60/2.75 inference(unit_resolution,[status(thm)],[250, 244, 231, 214])).
% 2.60/2.75 tff(252,plain,
% 2.60/2.75 (^[A: $i, B: $i] : refl((in(A, B) | empty(B) | (~element(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(253,plain,
% 2.60/2.75 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[252])).
% 2.60/2.75 tff(254,plain,
% 2.60/2.75 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(255,plain,
% 2.60/2.75 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (in(A, B) | empty(B) | (~element(A, B))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(256,plain,
% 2.60/2.75 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[255])).
% 2.60/2.75 tff(257,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 2.60/2.75 tff(258,plain,
% 2.60/2.75 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[257, 256])).
% 2.60/2.75 tff(259,plain,
% 2.60/2.75 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[258, 254])).
% 2.60/2.75 tff(260,plain,(
% 2.60/2.75 ![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 2.60/2.75 inference(skolemize,[status(sab)],[259])).
% 2.60/2.75 tff(261,plain,
% 2.60/2.75 (![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[260, 253])).
% 2.60/2.75 tff(262,plain,
% 2.60/2.75 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(263,plain,
% 2.60/2.75 ((in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9))) <=> (empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(264,plain,
% 2.60/2.75 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9))))),
% 2.60/2.75 inference(monotonicity,[status(thm)],[263])).
% 2.60/2.75 tff(265,plain,
% 2.60/2.75 (((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))) <=> ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 2.60/2.75 inference(transitivity,[status(thm)],[264, 262])).
% 2.60/2.75 tff(266,plain,
% 2.60/2.75 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | (in(tptp_fun_C_1(B!9, C!8), B!9) | empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 2.60/2.75 inference(quant_inst,[status(thm)],[])).
% 2.60/2.75 tff(267,plain,
% 2.60/2.75 ((~![A: $i, B: $i] : (in(A, B) | empty(B) | (~element(A, B)))) | empty(B!9) | in(tptp_fun_C_1(B!9, C!8), B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[266, 265])).
% 2.60/2.75 tff(268,plain,
% 2.60/2.75 (empty(B!9) | (~element(tptp_fun_C_1(B!9, C!8), B!9))),
% 2.60/2.75 inference(unit_resolution,[status(thm)],[267, 261, 190])).
% 2.60/2.75 tff(269,plain,
% 2.60/2.75 (~element(tptp_fun_C_1(B!9, C!8), B!9)),
% 2.60/2.75 inference(unit_resolution,[status(thm)],[268, 251])).
% 2.60/2.75 tff(270,plain,
% 2.60/2.75 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(271,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[270])).
% 2.60/2.75 tff(272,plain,
% 2.60/2.75 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(273,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[272])).
% 2.60/2.75 tff(274,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(275,plain,
% 2.60/2.75 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 2.60/2.75 inference(bind,[status(th)],[])).
% 2.60/2.75 tff(276,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 2.60/2.75 inference(quant_intro,[status(thm)],[275])).
% 2.60/2.75 tff(277,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 2.60/2.75 tff(278,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[277, 276])).
% 2.60/2.75 tff(279,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[278, 274])).
% 2.60/2.75 tff(280,plain,(
% 2.60/2.75 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 2.60/2.75 inference(skolemize,[status(sab)],[279])).
% 2.60/2.75 tff(281,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[280, 273])).
% 2.60/2.75 tff(282,plain,
% 2.60/2.75 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[281, 271])).
% 2.60/2.75 tff(283,plain,
% 2.60/2.75 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_rng(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(284,plain,
% 2.60/2.75 ((element(tptp_fun_C_1(B!9, C!8), B!9) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~element(relation_rng(C!8), powerset(B!9)))) <=> ((~element(relation_rng(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9))),
% 2.60/2.75 inference(rewrite,[status(thm)],[])).
% 2.60/2.75 tff(285,plain,
% 2.60/2.75 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_1(B!9, C!8), B!9) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~element(relation_rng(C!8), powerset(B!9))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(relation_rng(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9)))),
% 2.60/2.75 inference(monotonicity,[status(thm)],[284])).
% 2.60/2.75 tff(286,plain,
% 2.60/2.75 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_1(B!9, C!8), B!9) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~element(relation_rng(C!8), powerset(B!9))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9))),
% 2.60/2.75 inference(transitivity,[status(thm)],[285, 283])).
% 2.60/2.75 tff(287,plain,
% 2.60/2.75 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_1(B!9, C!8), B!9) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | (~element(relation_rng(C!8), powerset(B!9))))),
% 2.60/2.75 inference(quant_inst,[status(thm)],[])).
% 2.60/2.75 tff(288,plain,
% 2.60/2.75 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(relation_rng(C!8), powerset(B!9))) | (~in(tptp_fun_C_1(B!9, C!8), relation_rng(C!8))) | element(tptp_fun_C_1(B!9, C!8), B!9)),
% 2.60/2.75 inference(modus_ponens,[status(thm)],[287, 286])).
% 2.60/2.75 tff(289,plain,
% 2.60/2.75 ($false),
% 2.60/2.75 inference(unit_resolution,[status(thm)],[288, 282, 231, 269, 214])).
% 2.60/2.75 % SZS output end Proof
% 2.60/2.76 % E exiting
%------------------------------------------------------------------------------