%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC008-2.002 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:17:31 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MSC008-2.002 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 23:33:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(greek_type, type, (
% 0.12/0.39 greek: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(p2_type, type, (
% 0.12/0.39 p2: $i)).
% 0.12/0.39 tff(p1_type, type, (
% 0.12/0.39 p1: $i)).
% 0.12/0.39 tff(latin_type, type, (
% 0.12/0.39 latin: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(eq_type, type, (
% 0.12/0.39 eq: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(~greek(p1, p1, p1)), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[P: $i, O: $i] : refl((greek(p1, O, P) | greek(p2, O, P)) <=> (greek(p1, O, P) | greek(p2, O, P)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P)) <=> ![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P)) <=> ![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,axiom,(![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_row_required')).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 ![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p1, p1) | greek(p2, p1, p1))) <=> ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p1, p1) | greek(p2, p1, p1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p1, p1) | greek(p2, p1, p1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p1, p1) | greek(p2, p1, p1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (greek(p1, p1, p1) | greek(p2, p1, p1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (greek(p2, p1, p1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (^[N: $i, M: $i] : refl((greek(M, p1, N) | greek(M, p2, N)) <=> (greek(M, p1, N) | greek(M, p2, N)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N)) <=> ![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N)) <=> ![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(17,axiom,(![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_column_required')).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.39 tff(19,plain,(
% 0.12/0.39 ![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.12/0.39 inference(skolemize,[status(sab)],[18])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | (greek(p1, p1, p1) | greek(p1, p2, p1))) <=> ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | greek(p1, p1, p1) | greek(p1, p2, p1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | (greek(p1, p1, p1) | greek(p1, p2, p1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | greek(p1, p1, p1) | greek(p1, p2, p1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (greek(p1, p1, p1) | greek(p1, p2, p1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (greek(p1, p2, p1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[24, 1])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (^[B: $i, A: $i] : refl(((~eq(A, B)) | eq(B, A)) <=> ((~eq(A, B)) | eq(B, A)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A)) <=> ![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A)) <=> ![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(29,axiom,(![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry')).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.39 tff(31,plain,(
% 0.12/0.39 ![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.12/0.39 inference(skolemize,[status(sab)],[30])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~eq(p1, p2)) <=> (~eq(p1, p2))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,axiom,(~eq(p1, p2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p1_is_not_p2')).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (~eq(p1, p2)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))) | ((~eq(p2, p1)) | eq(p1, p2))) <=> ((~![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))) | (~eq(p2, p1)) | eq(p1, p2))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))) | ((~eq(p2, p1)) | eq(p1, p2))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))) | (~eq(p2, p1)) | eq(p1, p2)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (~eq(p2, p1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 35, 32])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (^[B: $i, D: $i, A: $i, C: $i] : refl((eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C))) <=> (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (^[B: $i, D: $i, A: $i, C: $i] : rewrite((((~greek(A, B, C)) | (~greek(D, B, C))) | eq(D, A)) <=> (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![B: $i, D: $i, A: $i, C: $i] : (((~greek(A, B, C)) | (~greek(D, B, C))) | eq(D, A)) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.39 tff(45,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((~greek(A, B, C)) | (~greek(D, B, C))) | eq(D, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_row_is_unique')).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.12/0.39 tff(48,plain,(
% 0.12/0.39 ![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[47])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | (eq(p2, p1) | (~greek(p1, p2, p1)) | (~greek(p2, p2, p1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | eq(p2, p1) | (~greek(p1, p2, p1)) | (~greek(p2, p2, p1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | (eq(p2, p1) | (~greek(p1, p2, p1)) | (~greek(p2, p2, p1)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | eq(p2, p1) | (~greek(p1, p2, p1)) | (~greek(p2, p2, p1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 ((~greek(p1, p2, p1)) | (~greek(p2, p2, p1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[52, 49, 39])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (~greek(p2, p2, p1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[53, 25])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (^[L: $i, K: $i] : refl((greek(K, L, p1) | greek(K, L, p2)) <=> (greek(K, L, p1) | greek(K, L, p2)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2)) <=> ![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2)) <=> ![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,axiom,(![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_cell_element')).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.40 tff(60,plain,(
% 0.12/0.40 ![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.12/0.40 inference(skolemize,[status(sab)],[59])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | (greek(p2, p2, p1) | greek(p2, p2, p2))) <=> ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | greek(p2, p2, p1) | greek(p2, p2, p2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | (greek(p2, p2, p1) | greek(p2, p2, p2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | greek(p2, p2, p1) | greek(p2, p2, p2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (greek(p2, p2, p2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[64, 61, 54])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | (greek(p1, p1, p1) | greek(p1, p1, p2))) <=> ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | greek(p1, p1, p1) | greek(p1, p1, p2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | (greek(p1, p1, p1) | greek(p1, p1, p2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | greek(p1, p1, p1) | greek(p1, p1, p2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (greek(p1, p1, p1) | greek(p1, p1, p2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[68, 61])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (greek(p1, p1, p2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[69, 1])).
% 0.12/0.40 tff(71,assumption,(greek(p2, p2, p2)), introduced(assumption)).
% 0.12/0.40 tff(72,assumption,(~latin(p2, p1, p1)), introduced(assumption)).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 (^[H: $i, G: $i] : refl((latin(G, p1, H) | latin(G, p2, H)) <=> (latin(G, p1, H) | latin(G, p2, H)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H)) <=> ![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H)) <=> ![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(76,axiom,(![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','latin_column_required')).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.40 tff(78,plain,(
% 0.12/0.40 ![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.12/0.40 inference(skolemize,[status(sab)],[77])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | (latin(p2, p1, p1) | latin(p2, p2, p1))) <=> ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | latin(p2, p1, p1) | latin(p2, p2, p1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | (latin(p2, p1, p1) | latin(p2, p2, p1))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | latin(p2, p1, p1) | latin(p2, p2, p1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (latin(p2, p2, p1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[82, 79, 72])).
% 0.12/0.40 tff(84,assumption,(greek(p1, p1, p2)), introduced(assumption)).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (^[I: $i, J: $i] : refl((latin(p1, I, J) | latin(p2, I, J)) <=> (latin(p1, I, J) | latin(p2, I, J)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J)) <=> ![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J)) <=> ![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(88,axiom,(![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','latin_row_required')).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.12/0.40 tff(90,plain,(
% 0.12/0.40 ![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.12/0.40 inference(skolemize,[status(sab)],[89])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | (latin(p1, p1, p1) | latin(p2, p1, p1))) <=> ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | latin(p1, p1, p1) | latin(p2, p1, p1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | (latin(p1, p1, p1) | latin(p2, p1, p1))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | latin(p1, p1, p1) | latin(p2, p1, p1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (latin(p1, p1, p1) | latin(p2, p1, p1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[94, 91])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (latin(p1, p1, p1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[95, 72])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (^[B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : refl((eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) <=> (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) <=> ![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[97])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) <=> ![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (^[B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) <=> ((~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))), (((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) | (~latin(E, F, D))) <=> (((~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) | (~latin(E, F, D))))), rewrite((((~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) | (~latin(E, F, D))) <=> ((~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))), (((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) | (~latin(E, F, D))) <=> ((~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))))), ((((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) | (~latin(E, F, D))) | eq(F, B)) <=> (((~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) | eq(F, B)))), rewrite((((~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) | eq(F, B)) <=> (eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))), ((((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) | (~latin(E, F, D))) | eq(F, B)) <=> (eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))))), (((((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) | (~latin(E, F, D))) | eq(F, B)) | eq(E, A)) <=> ((eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) | eq(E, A)))), rewrite(((eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C))) | eq(E, A)) <=> (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))), (((((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) | (~latin(E, F, D))) | eq(F, B)) | eq(E, A)) <=> (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : ((((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) | (~latin(E, F, D))) | eq(F, B)) | eq(E, A)) <=> ![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[100])).
% 0.12/0.40 tff(102,axiom,(![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : ((((((~greek(A, B, C)) | (~latin(A, B, D))) | (~greek(E, F, C))) | (~latin(E, F, D))) | eq(F, B)) | eq(E, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_two_same')).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 (![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.12/0.40 tff(105,plain,(
% 0.12/0.40 ![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[104])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 (![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~latin(p1, p1, p1)) | (~greek(p2, p2, p2)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~latin(p1, p1, p1)) | (~greek(p2, p2, p2)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 ((eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p1)) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p2))) <=> (eq(p1, p2) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~latin(p1, p1, p1)) | (~greek(p2, p2, p2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p1)) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p2)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~latin(p1, p1, p1)) | (~greek(p2, p2, p2))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p1)) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p2)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~latin(p1, p1, p1)) | (~greek(p2, p2, p2)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p1)) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p1)) | (~latin(p1, p1, p1)) | (~greek(p2, p2, p2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[112, 35, 106, 96, 84, 83, 71])).
% 0.21/0.41 tff(114,plain,(latin(p2, p1, p1) | (~greek(p1, p1, p2)) | (~greek(p2, p2, p2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 (latin(p2, p1, p1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[114, 70, 65])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C))) <=> ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 (![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 (![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 (^[B: $i, D: $i, A: $i, C: $i] : rewrite((((~latin(A, B, C)) | (~latin(D, B, C))) | eq(D, A)) <=> ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 (![B: $i, D: $i, A: $i, C: $i] : (((~latin(A, B, C)) | (~latin(D, B, C))) | eq(D, A)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.41 tff(121,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((~latin(A, B, C)) | (~latin(D, B, C))) | eq(D, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','latin_row_is_unique')).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 (![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.41 tff(124,plain,(
% 0.21/0.41 ![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[123])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 (![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 (((~![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))) | (eq(p2, p1) | (~latin(p2, p1, p1)) | (~latin(p1, p1, p1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))) | eq(p2, p1) | (~latin(p2, p1, p1)) | (~latin(p1, p1, p1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 (((~latin(p1, p1, p1)) | eq(p2, p1) | (~latin(p2, p1, p1))) <=> (eq(p2, p1) | (~latin(p2, p1, p1)) | (~latin(p1, p1, p1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 (((~![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))) | ((~latin(p1, p1, p1)) | eq(p2, p1) | (~latin(p2, p1, p1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))) | (eq(p2, p1) | (~latin(p2, p1, p1)) | (~latin(p1, p1, p1))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 (((~![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))) | ((~latin(p1, p1, p1)) | eq(p2, p1) | (~latin(p2, p1, p1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))) | eq(p2, p1) | (~latin(p2, p1, p1)) | (~latin(p1, p1, p1)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 ((~![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))) | ((~latin(p1, p1, p1)) | eq(p2, p1) | (~latin(p2, p1, p1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 ((~![B: $i, D: $i, A: $i, C: $i] : ((~latin(A, B, C)) | eq(D, A) | (~latin(D, B, C)))) | eq(p2, p1) | (~latin(p2, p1, p1)) | (~latin(p1, p1, p1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 ((~latin(p2, p1, p1)) | (~latin(p1, p1, p1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[131, 125, 39])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 (~latin(p1, p1, p1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[132, 115])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 (((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | (latin(p1, p1, p1) | latin(p1, p2, p1))) <=> ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | latin(p1, p1, p1) | latin(p1, p2, p1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(135,plain,
% 0.21/0.41 ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | (latin(p1, p1, p1) | latin(p1, p2, p1))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | latin(p1, p1, p1) | latin(p1, p2, p1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 (latin(p1, p1, p1) | latin(p1, p2, p1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[136, 79])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 (latin(p1, p2, p1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[137, 133])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~greek(p2, p1, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | eq(p2, p1) | (~greek(p2, p1, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 ((eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~greek(p2, p1, p1))) <=> (eq(p1, p2) | eq(p2, p1) | (~greek(p2, p1, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~greek(p2, p1, p1)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~greek(p2, p1, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~greek(p2, p1, p1)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | eq(p2, p1) | (~greek(p2, p1, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[141, 139])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~greek(p2, p1, p1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | eq(p2, p1) | (~greek(p2, p1, p1)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.21/0.42 tff(145,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[144, 35, 106, 39, 138, 115, 25, 13])).
% 0.21/0.42 tff(146,plain,(greek(p1, p1, p1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 (^[B: $i, D: $i, A: $i, C: $i] : refl((eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C))) <=> (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 (^[B: $i, D: $i, A: $i, C: $i] : rewrite((((~greek(A, B, C)) | (~greek(A, B, D))) | eq(D, C)) <=> (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (((~greek(A, B, C)) | (~greek(A, B, D))) | eq(D, C)) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.42 tff(152,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((~greek(A, B, C)) | (~greek(A, B, D))) | eq(D, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_element_is_unique')).
% 0.21/0.42 tff(153,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.42 tff(154,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.21/0.42 tff(155,plain,(
% 0.21/0.42 ![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[154])).
% 0.21/0.42 tff(156,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.21/0.42 tff(157,plain,
% 0.21/0.42 (((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p1, p2)) | (~greek(p1, p1, p1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~greek(p1, p1, p2)) | (~greek(p1, p1, p1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(158,plain,
% 0.21/0.42 ((eq(p1, p2) | (~greek(p1, p1, p1)) | (~greek(p1, p1, p2))) <=> (eq(p1, p2) | (~greek(p1, p1, p2)) | (~greek(p1, p1, p1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(159,plain,
% 0.21/0.42 (((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p1, p1)) | (~greek(p1, p1, p2)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p1, p2)) | (~greek(p1, p1, p1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[158])).
% 0.21/0.42 tff(160,plain,
% 0.21/0.42 (((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p1, p1)) | (~greek(p1, p1, p2)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~greek(p1, p1, p2)) | (~greek(p1, p1, p1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[159, 157])).
% 0.21/0.42 tff(161,plain,
% 0.21/0.42 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p1, p1)) | (~greek(p1, p1, p2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(162,plain,
% 0.21/0.42 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~greek(p1, p1, p2)) | (~greek(p1, p1, p1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.42 tff(163,plain,
% 0.21/0.42 ((~greek(p1, p1, p2)) | (~greek(p1, p1, p1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[162, 35, 156])).
% 0.21/0.42 tff(164,plain,
% 0.21/0.42 (~greek(p1, p1, p2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[163, 146])).
% 0.21/0.42 tff(165,plain,
% 0.21/0.42 (((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p1, p2) | greek(p2, p1, p2))) <=> ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p1, p2) | greek(p2, p1, p2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(166,plain,
% 0.21/0.42 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p1, p2) | greek(p2, p1, p2))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(167,plain,
% 0.21/0.42 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p1, p2) | greek(p2, p1, p2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.42 tff(168,plain,
% 0.21/0.42 (greek(p2, p1, p2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[167, 8, 164])).
% 0.21/0.42 tff(169,plain,
% 0.21/0.42 (((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | (greek(p1, p1, p2) | greek(p1, p2, p2))) <=> ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | greek(p1, p1, p2) | greek(p1, p2, p2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(170,plain,
% 0.21/0.42 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | (greek(p1, p1, p2) | greek(p1, p2, p2))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(171,plain,
% 0.21/0.42 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | greek(p1, p1, p2) | greek(p1, p2, p2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.42 tff(172,plain,
% 0.21/0.42 (greek(p1, p2, p2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[171, 20, 164])).
% 0.21/0.42 tff(173,plain,
% 0.21/0.42 (^[B: $i, D: $i, A: $i, C: $i] : refl((eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C))) <=> (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(174,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.42 tff(175,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(176,plain,
% 0.21/0.42 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(rewrite(((~greek(A, B, C)) | (~greek(A, D, C))) <=> ((~greek(A, B, C)) | (~greek(A, D, C)))), ((((~greek(A, B, C)) | (~greek(A, D, C))) | eq(D, B)) <=> (((~greek(A, B, C)) | (~greek(A, D, C))) | eq(D, B)))), rewrite((((~greek(A, B, C)) | (~greek(A, D, C))) | eq(D, B)) <=> (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))), ((((~greek(A, B, C)) | (~greek(A, D, C))) | eq(D, B)) <=> (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(177,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (((~greek(A, B, C)) | (~greek(A, D, C))) | eq(D, B)) <=> ![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[176])).
% 0.21/0.42 tff(178,axiom,(![B: $i, D: $i, A: $i, C: $i] : (((~greek(A, B, C)) | (~greek(A, D, C))) | eq(D, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_column_is_unique')).
% 0.21/0.42 tff(179,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.42 tff(180,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.21/0.42 tff(181,plain,(
% 0.21/0.42 ![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[180])).
% 0.21/0.42 tff(182,plain,
% 0.21/0.42 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.21/0.42 tff(183,plain,
% 0.21/0.42 (((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))) | (eq(p1, p2) | (~greek(p1, p2, p1)) | (~greek(p1, p1, p1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))) | eq(p1, p2) | (~greek(p1, p2, p1)) | (~greek(p1, p1, p1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(184,plain,
% 0.21/0.42 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))) | (eq(p1, p2) | (~greek(p1, p2, p1)) | (~greek(p1, p1, p1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(185,plain,
% 0.21/0.42 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, B) | (~greek(A, B, C)) | (~greek(A, D, C)))) | eq(p1, p2) | (~greek(p1, p2, p1)) | (~greek(p1, p1, p1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.42 tff(186,plain,
% 0.21/0.42 ((~greek(p1, p2, p1)) | (~greek(p1, p1, p1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[185, 35, 182])).
% 0.21/0.42 tff(187,plain,
% 0.21/0.42 (~greek(p1, p2, p1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[186, 146])).
% 0.21/0.42 tff(188,plain,
% 0.21/0.42 (((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p2, p1) | greek(p2, p2, p1))) <=> ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p2, p1) | greek(p2, p2, p1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(189,plain,
% 0.21/0.42 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p2, p1) | greek(p2, p2, p1))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(190,plain,
% 0.21/0.42 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p2, p1) | greek(p2, p2, p1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.42 tff(191,plain,
% 0.21/0.42 (greek(p2, p2, p1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[190, 8, 187])).
% 0.21/0.42 tff(192,plain,
% 0.21/0.42 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)) | (~greek(p1, p1, p1)) | (~latin(p1, p1, p1)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)) | (~greek(p1, p1, p1)) | (~latin(p1, p1, p1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(193,plain,
% 0.21/0.42 ((eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p1)) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1))) <=> (eq(p1, p2) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)) | (~greek(p1, p1, p1)) | (~latin(p1, p1, p1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(194,plain,
% 0.21/0.42 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p1)) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)) | (~greek(p1, p1, p1)) | (~latin(p1, p1, p1))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[193])).
% 0.21/0.43 tff(195,plain,
% 0.21/0.43 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p1)) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)) | (~greek(p1, p1, p1)) | (~latin(p1, p1, p1)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[194, 192])).
% 0.21/0.43 tff(196,plain,
% 0.21/0.43 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p1)) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(197,plain,
% 0.21/0.43 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~latin(p2, p2, p1)) | (~greek(p2, p2, p1)) | (~greek(p1, p1, p1)) | (~latin(p1, p1, p1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.21/0.43 tff(198,plain,
% 0.21/0.43 ((~latin(p2, p2, p1)) | (~greek(p2, p2, p1)) | (~greek(p1, p1, p1)) | (~latin(p1, p1, p1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[197, 35, 106])).
% 0.21/0.43 tff(199,plain,
% 0.21/0.43 ((~latin(p2, p2, p1)) | (~latin(p1, p1, p1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[198, 146, 191])).
% 0.21/0.43 tff(200,plain,
% 0.21/0.43 (~latin(p2, p2, p1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[199, 96])).
% 0.21/0.43 tff(201,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[82, 79, 72, 200])).
% 0.21/0.43 tff(202,plain,(latin(p2, p1, p1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(203,plain,
% 0.21/0.43 (~latin(p1, p1, p1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[132, 202])).
% 0.21/0.43 tff(204,plain,
% 0.21/0.43 (latin(p1, p2, p1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[137, 203])).
% 0.21/0.43 tff(205,plain,
% 0.21/0.43 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)) | (~greek(p2, p1, p2)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | eq(p2, p1) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)) | (~greek(p2, p1, p2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(206,plain,
% 0.21/0.43 ((eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p1)) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~greek(p2, p1, p2))) <=> (eq(p1, p2) | eq(p2, p1) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)) | (~greek(p2, p1, p2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(207,plain,
% 0.21/0.43 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p1)) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~greek(p2, p1, p2)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)) | (~greek(p2, p1, p2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[206])).
% 0.21/0.43 tff(208,plain,
% 0.21/0.43 (((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p1)) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~greek(p2, p1, p2)))) <=> ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | eq(p2, p1) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)) | (~greek(p2, p1, p2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[207, 205])).
% 0.21/0.43 tff(209,plain,
% 0.21/0.43 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p1)) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~greek(p2, p1, p2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(210,plain,
% 0.21/0.43 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | eq(p2, p1) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p1)) | (~latin(p1, p2, p1)) | (~greek(p2, p1, p2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.21/0.43 tff(211,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[210, 35, 106, 39, 204, 202, 172, 168])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------