TSTP Solution File: MSC008-2.002 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MSC008-2.002 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Sun Sep 18 05:34:03 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MSC008-2.002 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 03:15:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(greek_type, type, (
% 0.19/0.41 greek: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(p1_type, type, (
% 0.19/0.41 p1: $i)).
% 0.19/0.41 tff(p2_type, type, (
% 0.19/0.41 p2: $i)).
% 0.19/0.41 tff(latin_type, type, (
% 0.19/0.41 latin: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(eq_type, type, (
% 0.19/0.41 eq: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,assumption,(greek(p1, p2, p1)), introduced(assumption)).
% 0.19/0.41 tff(2,assumption,(~greek(p1, p2, p2)), introduced(assumption)).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (^[N: $i, M: $i] : refl((greek(M, p1, N) | greek(M, p2, N)) <=> (greek(M, p1, N) | greek(M, p2, N)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N)) <=> ![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N)) <=> ![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(6,axiom,(![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_column_required')).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.41 tff(8,plain,(
% 0.19/0.41 ![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.19/0.41 inference(skolemize,[status(sab)],[7])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | (greek(p1, p1, p2) | greek(p1, p2, p2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | greek(p1, p1, p2) | greek(p1, p2, p2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (greek(p1, p1, p2) | greek(p1, p2, p2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (greek(p1, p1, p2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[13, 2])).
% 0.19/0.41 tff(15,assumption,(greek(p1, p1, p2)), introduced(assumption)).
% 0.19/0.41 tff(16,assumption,(greek(p2, p1, p2)), introduced(assumption)).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl(((~eq(A, B)) | eq(B, A)) <=> ((~eq(A, B)) | eq(B, A)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A)) <=> ![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A)) <=> ![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(20,axiom,(![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry')).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.41 tff(22,plain,(
% 0.19/0.41 ![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.19/0.41 inference(skolemize,[status(sab)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~eq(p1, p2)) <=> (~eq(p1, p2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(25,axiom,(~eq(p1, p2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p1_is_not_p2')).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (~eq(p1, p2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))) | ((~eq(p2, p1)) | eq(p1, p2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~eq(A, B)) | eq(B, A))) | (~eq(p2, p1)) | eq(p1, p2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (~eq(p2, p1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[29, 26, 23])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.41 tff(36,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')).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.41 tff(39,plain,(
% 0.19/0.41 ![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[38])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | (eq(p2, p1) | (~greek(p1, p1, p2)) | (~greek(p2, p1, p2)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | eq(p2, p1) | (~greek(p1, p1, p2)) | (~greek(p2, p1, p2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | (eq(p2, p1) | (~greek(p1, p1, p2)) | (~greek(p2, p1, p2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | eq(p2, p1) | (~greek(p1, p1, p2)) | (~greek(p2, p1, p2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 40, 30, 16, 15])).
% 0.19/0.41 tff(45,plain,((~greek(p2, p1, p2)) | (~greek(p1, p1, p2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (~greek(p2, p1, p2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[45, 14])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (^[L: $i, K: $i] : refl((greek(K, L, p1) | greek(K, L, p2)) <=> (greek(K, L, p1) | greek(K, L, p2)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2)) <=> ![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2)) <=> ![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(50,axiom,(![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_cell_element')).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,(
% 0.19/0.41 ![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.19/0.41 inference(skolemize,[status(sab)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | (greek(p2, p1, p1) | greek(p2, p1, p2))) <=> ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | greek(p2, p1, p1) | greek(p2, p1, p2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | (greek(p2, p1, p1) | greek(p2, p1, p2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | greek(p2, p1, p1) | greek(p2, p1, p2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (greek(p2, p1, p1) | greek(p2, p1, p2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (greek(p2, p1, p1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 46])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | (greek(p1, p2, p1) | greek(p1, p2, p2))) <=> ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | greek(p1, p2, p1) | greek(p1, p2, p2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | (greek(p1, p2, p1) | greek(p1, p2, p2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~![L: $i, K: $i] : (greek(K, L, p1) | greek(K, L, p2))) | greek(p1, p2, p1) | greek(p1, p2, p2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (greek(p1, p2, p1) | greek(p1, p2, p2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 53])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (greek(p1, p2, p1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[62, 2])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (^[P: $i, O: $i] : refl((greek(p1, O, P) | greek(p2, O, P)) <=> (greek(p1, O, P) | greek(p2, O, P)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P)) <=> ![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P)) <=> ![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(67,axiom,(![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','greek_row_required')).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.41 tff(69,plain,(
% 0.19/0.41 ![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.19/0.41 inference(skolemize,[status(sab)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p2, p2) | greek(p2, p2, p2))) <=> ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p2, p2) | greek(p2, p2, p2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p2, p2) | greek(p2, p2, p2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p2, p2) | greek(p2, p2, p2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (greek(p1, p2, p2) | greek(p2, p2, p2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (greek(p2, p2, p2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[74, 2])).
% 0.19/0.41 tff(76,assumption,(~latin(p1, p2, p2)), introduced(assumption)).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (^[H: $i, G: $i] : refl((latin(G, p1, H) | latin(G, p2, H)) <=> (latin(G, p1, H) | latin(G, p2, H)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H)) <=> ![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H)) <=> ![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(80,axiom,(![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','latin_column_required')).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.42 tff(82,plain,(
% 0.19/0.42 ![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.19/0.42 inference(skolemize,[status(sab)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | (latin(p1, p1, p2) | latin(p1, p2, p2))) <=> ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | latin(p1, p1, p2) | latin(p1, p2, p2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | (latin(p1, p1, p2) | latin(p1, p2, p2))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | latin(p1, p1, p2) | latin(p1, p2, p2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (latin(p1, p1, p2) | latin(p1, p2, p2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (latin(p1, p1, p2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 76])).
% 0.19/0.42 tff(89,assumption,(greek(p2, p2, p2)), introduced(assumption)).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (^[I: $i, J: $i] : refl((latin(p1, I, J) | latin(p2, I, J)) <=> (latin(p1, I, J) | latin(p2, I, J)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J)) <=> ![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J)) <=> ![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(93,axiom,(![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','latin_row_required')).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.42 tff(95,plain,(
% 0.19/0.42 ![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.19/0.42 inference(skolemize,[status(sab)],[94])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | (latin(p1, p2, p2) | latin(p2, p2, p2))) <=> ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | latin(p1, p2, p2) | latin(p2, p2, p2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | (latin(p1, p2, p2) | latin(p2, p2, p2))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | latin(p1, p2, p2) | latin(p2, p2, p2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (latin(p1, p2, p2) | latin(p2, p2, p2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (latin(p2, p2, p2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[100, 76])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (![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))) <=> ![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (![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))) <=> ![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.42 tff(107,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')).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.42 tff(110,plain,(
% 0.19/0.42 ![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)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[109])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (((~![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, p2)) | (~greek(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p1, 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) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p1, p1, p2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((eq(p1, p2) | eq(p1, p2) | (~latin(p1, p1, p2)) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p2))) <=> (eq(p1, p2) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p1, p1, p2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (((~![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, p2)) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p2)) | (~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) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p1, p1, p2))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (((~![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, p2)) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p2)) | (~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) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p1, p1, p2)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[114, 112])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 ((~![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, p2)) | (~greek(p1, p1, p2)) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p1, p1, p2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[117, 26, 111, 101, 89, 88, 15])).
% 0.19/0.43 tff(119,plain,(latin(p1, p2, p2) | (~greek(p2, p2, p2)) | (~greek(p1, p1, p2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (latin(p1, p2, p2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[119, 75, 14])).
% 0.19/0.43 tff(121,assumption,(greek(p2, p1, p1)), introduced(assumption)).
% 0.19/0.43 tff(122,assumption,(latin(p1, p2, p2)), introduced(assumption)).
% 0.19/0.43 tff(123,assumption,(latin(p2, p1, p2)), introduced(assumption)).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (((~![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, p2)) | (~latin(p2, p1, p2)) | (~greek(p1, p2, 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) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p1, p2, p1)) | (~greek(p2, p1, p1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 ((eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p2)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p1))) <=> (eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p1, p2, p1)) | (~greek(p2, p1, p1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (((~![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, p2)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p2)) | (~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) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p1, p2, p1)) | (~greek(p2, p1, p1))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (((~![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, p2)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p2)) | (~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) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p1, p2, p1)) | (~greek(p2, p1, p1)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 ((~![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, p2)) | (~greek(p1, p2, p1)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p1, p2, p1)) | (~greek(p2, p1, p1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[129, 26, 111, 30, 123, 122, 1, 121])).
% 0.19/0.43 tff(131,plain,((~latin(p2, p1, p2)) | (~latin(p1, p2, p2)) | (~greek(p1, p2, p1)) | (~greek(p2, p1, p1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 (~latin(p2, p1, p2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[131, 120, 63, 58])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | (latin(p1, p1, p2) | latin(p2, p1, p2))) <=> ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | latin(p1, p1, p2) | latin(p2, p1, p2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | (latin(p1, p1, p2) | latin(p2, p1, p2))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(135,plain,
% 0.19/0.43 ((~![I: $i, J: $i] : (latin(p1, I, J) | latin(p2, I, J))) | latin(p1, p1, p2) | latin(p2, p1, p2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.43 tff(136,plain,
% 0.19/0.43 (latin(p1, p1, p2) | latin(p2, p1, p2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[135, 96])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (latin(p1, p1, p2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[136, 132])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 (((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | (latin(p2, p1, p2) | latin(p2, p2, p2))) <=> ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | latin(p2, p1, p2) | latin(p2, p2, p2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | (latin(p2, p1, p2) | latin(p2, p2, p2))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 ((~![H: $i, G: $i] : (latin(G, p1, H) | latin(G, p2, H))) | latin(p2, p1, p2) | latin(p2, p2, p2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 (latin(p2, p1, p2) | latin(p2, p2, p2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[140, 83])).
% 0.19/0.43 tff(142,plain,
% 0.19/0.43 (latin(p2, p2, p2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[141, 132])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[117, 26, 111, 142, 75, 137, 14])).
% 0.19/0.43 tff(144,plain,(greek(p1, p2, p2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[145])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.43 tff(150,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')).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.19/0.43 tff(153,plain,(
% 0.19/0.43 ![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[152])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p2, p1)) | (~greek(p1, p2, 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, p2, p1)) | (~greek(p1, p2, p2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | (eq(p1, p2) | (~greek(p1, p2, p1)) | (~greek(p1, p2, p2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, C) | (~greek(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | (~greek(p1, p2, p1)) | (~greek(p1, p2, p2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[157, 26, 154, 144, 1])).
% 0.19/0.43 tff(159,plain,(~greek(p1, p2, p1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | (eq(p2, p1) | (~greek(p2, p2, p2)) | (~greek(p1, p2, p2)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | eq(p2, p1) | (~greek(p2, p2, p2)) | (~greek(p1, p2, p2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 ((eq(p2, p1) | (~greek(p1, p2, p2)) | (~greek(p2, p2, p2))) <=> (eq(p2, p1) | (~greek(p2, p2, p2)) | (~greek(p1, p2, p2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 (((~![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, p2)) | (~greek(p2, p2, p2)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | (eq(p2, p1) | (~greek(p2, p2, p2)) | (~greek(p1, p2, p2))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[161])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 (((~![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, p2)) | (~greek(p2, p2, p2)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | eq(p2, p1) | (~greek(p2, p2, p2)) | (~greek(p1, p2, p2)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[162, 160])).
% 0.19/0.44 tff(164,plain,
% 0.19/0.44 ((~![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, p2)) | (~greek(p2, p2, p2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(165,plain,
% 0.19/0.44 ((~![B: $i, D: $i, A: $i, C: $i] : (eq(D, A) | (~greek(A, B, C)) | (~greek(D, B, C)))) | eq(p2, p1) | (~greek(p2, p2, p2)) | (~greek(p1, p2, p2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.44 tff(166,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[165, 40, 30, 89, 144])).
% 0.19/0.44 tff(167,plain,(~greek(p2, p2, p2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(168,plain,
% 0.19/0.44 (((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | (greek(p2, p1, p2) | greek(p2, p2, p2))) <=> ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | greek(p2, p1, p2) | greek(p2, p2, p2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | (greek(p2, p1, p2) | greek(p2, p2, p2))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(170,plain,
% 0.19/0.44 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | greek(p2, p1, p2) | greek(p2, p2, p2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.44 tff(171,plain,
% 0.19/0.44 (greek(p2, p1, p2) | greek(p2, p2, p2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[170, 9])).
% 0.19/0.44 tff(172,plain,
% 0.19/0.44 (greek(p2, p1, p2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[171, 167])).
% 0.19/0.44 tff(173,assumption,(latin(p1, p1, p2)), introduced(assumption)).
% 0.19/0.44 tff(174,assumption,(~greek(p1, p2, p1)), introduced(assumption)).
% 0.19/0.44 tff(175,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(176,plain,
% 0.19/0.44 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | (greek(p1, p2, p1) | greek(p2, p2, p1))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(177,plain,
% 0.19/0.44 ((~![P: $i, O: $i] : (greek(p1, O, P) | greek(p2, O, P))) | greek(p1, p2, p1) | greek(p2, p2, p1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.44 tff(178,plain,
% 0.19/0.44 (greek(p1, p2, p1) | greek(p2, p2, p1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[177, 70])).
% 0.19/0.44 tff(179,plain,
% 0.19/0.44 (greek(p2, p2, p1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[178, 174])).
% 0.19/0.44 tff(180,assumption,(latin(p2, p2, p2)), introduced(assumption)).
% 0.19/0.44 tff(181,plain,
% 0.19/0.44 (((~![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(p2, p1) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~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(p2, p1) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p2, p2, p1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(182,plain,
% 0.19/0.44 ((eq(p2, p1) | eq(p2, p1) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p1)) | (~latin(p1, p1, p2)) | (~greek(p1, p1, p1))) <=> (eq(p2, p1) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p2, p2, p1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(183,plain,
% 0.19/0.44 (((~![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(p2, p1) | eq(p2, p1) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p1)) | (~latin(p1, p1, p2)) | (~greek(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(p2, p1) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p2, p2, p1))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[182])).
% 0.19/0.44 tff(184,plain,
% 0.19/0.44 (((~![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(p2, p1) | eq(p2, p1) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p1)) | (~latin(p1, p1, p2)) | (~greek(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(p2, p1) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p2, p2, p1)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[183, 181])).
% 0.19/0.44 tff(185,plain,
% 0.19/0.44 ((~![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(p2, p1) | eq(p2, p1) | (~latin(p2, p2, p2)) | (~greek(p2, p2, p1)) | (~latin(p1, p1, p2)) | (~greek(p1, p1, p1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(186,plain,
% 0.19/0.44 ((~![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(p2, p1) | (~greek(p1, p1, p1)) | (~latin(p2, p2, p2)) | (~latin(p1, p1, p2)) | (~greek(p2, p2, p1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.19/0.44 tff(187,plain,
% 0.19/0.44 (~greek(p1, p1, p1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[186, 111, 30, 180, 179, 173])).
% 0.19/0.44 tff(188,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(189,plain,
% 0.19/0.44 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | (greek(p1, p1, p1) | greek(p1, p2, p1))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(190,plain,
% 0.19/0.44 ((~![N: $i, M: $i] : (greek(M, p1, N) | greek(M, p2, N))) | greek(p1, p1, p1) | greek(p1, p2, p1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.44 tff(191,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[190, 9, 174, 187])).
% 0.19/0.44 tff(192,plain,(greek(p1, p2, p1) | (~latin(p2, p2, p2)) | (~latin(p1, p1, p2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(193,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[192, 88, 101, 159])).
% 0.19/0.44 tff(194,plain,(latin(p1, p2, p2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(195,plain,
% 0.19/0.44 (((~![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, p2)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p2)) | (~greek(p1, 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) | eq(p2, p1) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p2)) | (~greek(p1, p2, p2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(196,plain,
% 0.19/0.44 ((eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p2)) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p2))) <=> (eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p2)) | (~greek(p1, p2, p2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(197,plain,
% 0.19/0.44 (((~![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, p2)) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~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) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p2)) | (~greek(p1, p2, p2))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[196])).
% 0.19/0.44 tff(198,plain,
% 0.19/0.44 (((~![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, p2)) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~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) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p2)) | (~greek(p1, p2, p2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[197, 195])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 ((~![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, p2)) | (~greek(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 ((~![B: $i, D: $i, A: $i, E: $i, F: $i, C: $i] : (eq(E, A) | eq(F, B) | (~latin(E, F, D)) | (~greek(E, F, C)) | (~latin(A, B, D)) | (~greek(A, B, C)))) | eq(p1, p2) | eq(p2, p1) | (~latin(p1, p2, p2)) | (~latin(p2, p1, p2)) | (~greek(p2, p1, p2)) | (~greek(p1, p2, p2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[200, 26, 111, 30, 123, 194, 172, 144])).
% 0.19/0.45 tff(202,plain,(~latin(p2, p1, p2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(203,plain,
% 0.19/0.45 (latin(p2, p2, p2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[141, 202])).
% 0.19/0.45 tff(204,plain,
% 0.19/0.45 (latin(p1, p1, p2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[136, 202])).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[192, 204, 203, 159])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------