TSTP Solution File: MSC008-1.002 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MSC008-1.002 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Mon May 22 16:35:10 EDT 2023
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MSC008-1.002 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 : Mon May 22 16:57:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(greek_type, type, (
% 0.20/0.41 greek: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(p_2_type, type, (
% 0.20/0.41 p_2: $i)).
% 0.20/0.41 tff(p_1_type, type, (
% 0.20/0.41 p_1: $i)).
% 0.20/0.41 tff(latin_type, type, (
% 0.20/0.41 latin: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(eq_type, type, (
% 0.20/0.41 eq: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,assumption,(~greek(p_1, p_2, p_2)), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[Row: $i, Label: $i] : refl((greek(Row, p_1, Label) | greek(Row, p_2, Label)) <=> (greek(Row, p_1, Label) | greek(Row, p_2, Label)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label)) <=> ![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label)) <=> ![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','greek_column_required')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | (greek(p_1, p_1, p_2) | greek(p_1, p_2, p_2))) <=> ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | greek(p_1, p_1, p_2) | greek(p_1, p_2, p_2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | (greek(p_1, p_1, p_2) | greek(p_1, p_2, p_2))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | greek(p_1, p_1, p_2) | greek(p_1, p_2, p_2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (greek(p_1, p_1, p_2) | greek(p_1, p_2, p_2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (greek(p_1, p_1, p_2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (^[Row: $i, Column: $i] : refl((greek(Row, Column, p_1) | greek(Row, Column, p_2)) <=> (greek(Row, Column, p_1) | greek(Row, Column, p_2)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2)) <=> ![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2)) <=> ![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(17,axiom,(![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','greek_cell_element')).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,(
% 0.20/0.41 ![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))),
% 0.20/0.41 inference(skolemize,[status(sab)],[18])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | (greek(p_1, p_2, p_1) | greek(p_1, p_2, p_2))) <=> ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | greek(p_1, p_2, p_1) | greek(p_1, p_2, p_2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | (greek(p_1, p_2, p_1) | greek(p_1, p_2, p_2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | greek(p_1, p_2, p_1) | greek(p_1, p_2, p_2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (greek(p_1, p_2, p_1) | greek(p_1, p_2, p_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (greek(p_1, p_2, p_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[24, 1])).
% 0.20/0.42 tff(26,assumption,(greek(p_1, p_1, p_2)), introduced(assumption)).
% 0.20/0.42 tff(27,assumption,(greek(p_2, p_1, p_2)), introduced(assumption)).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (^[Y: $i, X: $i] : refl(((~eq(X, Y)) | eq(Y, X)) <=> ((~eq(X, Y)) | eq(Y, X)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X)) <=> ![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X)) <=> ![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(31,axiom,(![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry')).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.42 tff(33,plain,(
% 0.20/0.42 ![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.20/0.42 inference(skolemize,[status(sab)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 ((~eq(p_1, p_2)) <=> (~eq(p_1, p_2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(36,axiom,(~eq(p_1, p_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p_1_is_not_p_2')).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (~eq(p_1, p_2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (((~![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))) | ((~eq(p_2, p_1)) | eq(p_1, p_2))) <=> ((~![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))) | (~eq(p_2, p_1)) | eq(p_1, p_2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))) | ((~eq(p_2, p_1)) | eq(p_1, p_2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 ((~![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))) | (~eq(p_2, p_1)) | eq(p_1, p_2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (~eq(p_2, p_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[40, 37, 34])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (^[Row2: $i, Row1: $i, Column: $i, Label: $i] : refl((eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label))) <=> (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label))) <=> ![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label))) <=> ![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (^[Row2: $i, Row1: $i, Column: $i, Label: $i] : rewrite((((~greek(Row1, Column, Label)) | (~greek(Row2, Column, Label))) | eq(Row1, Row2)) <=> (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![Row2: $i, Row1: $i, Column: $i, Label: $i] : (((~greek(Row1, Column, Label)) | (~greek(Row2, Column, Label))) | eq(Row1, Row2)) <=> ![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42 tff(47,axiom,(![Row2: $i, Row1: $i, Column: $i, Label: $i] : (((~greek(Row1, Column, Label)) | (~greek(Row2, Column, Label))) | eq(Row1, Row2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','greek_row_is_unique')).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.42 tff(50,plain,(
% 0.20/0.42 ![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[49])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | (eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_1, p_2)))) <=> ((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_1, p_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 ((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | (eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_1, p_2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 ((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_1, p_2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[54, 51, 41, 27, 26])).
% 0.20/0.42 tff(56,plain,((~greek(p_2, p_1, p_2)) | (~greek(p_1, p_1, p_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (~greek(p_2, p_1, p_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[56, 13])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | (greek(p_2, p_1, p_1) | greek(p_2, p_1, p_2))) <=> ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | greek(p_2, p_1, p_1) | greek(p_2, p_1, p_2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | (greek(p_2, p_1, p_1) | greek(p_2, p_1, p_2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | greek(p_2, p_1, p_1) | greek(p_2, p_1, p_2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (greek(p_2, p_1, p_1) | greek(p_2, p_1, p_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 20])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (greek(p_2, p_1, p_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 57])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (^[Column: $i, Label: $i] : refl((greek(p_1, Column, Label) | greek(p_2, Column, Label)) <=> (greek(p_1, Column, Label) | greek(p_2, Column, Label)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label)) <=> ![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label)) <=> ![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(66,axiom,(![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','greek_row_required')).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.42 tff(68,plain,(
% 0.20/0.42 ![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))),
% 0.20/0.42 inference(skolemize,[status(sab)],[67])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | (greek(p_1, p_2, p_2) | greek(p_2, p_2, p_2))) <=> ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | greek(p_1, p_2, p_2) | greek(p_2, p_2, p_2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | (greek(p_1, p_2, p_2) | greek(p_2, p_2, p_2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | greek(p_1, p_2, p_2) | greek(p_2, p_2, p_2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (greek(p_1, p_2, p_2) | greek(p_2, p_2, p_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (greek(p_2, p_2, p_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 1])).
% 0.20/0.42 tff(75,assumption,(~latin(p_1, p_2, p_2)), introduced(assumption)).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (^[Row: $i, Label: $i] : refl((latin(Row, p_1, Label) | latin(Row, p_2, Label)) <=> (latin(Row, p_1, Label) | latin(Row, p_2, Label)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label)) <=> ![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label)) <=> ![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(79,axiom,(![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','latin_column_required')).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.42 tff(81,plain,(
% 0.20/0.42 ![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))),
% 0.20/0.42 inference(skolemize,[status(sab)],[80])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | (latin(p_1, p_1, p_2) | latin(p_1, p_2, p_2))) <=> ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | latin(p_1, p_1, p_2) | latin(p_1, p_2, p_2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | (latin(p_1, p_1, p_2) | latin(p_1, p_2, p_2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | latin(p_1, p_1, p_2) | latin(p_1, p_2, p_2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (latin(p_1, p_1, p_2) | latin(p_1, p_2, p_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (latin(p_1, p_1, p_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.20/0.42 tff(88,assumption,(greek(p_2, p_2, p_2)), introduced(assumption)).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (^[Column: $i, Label: $i] : refl((latin(p_1, Column, Label) | latin(p_2, Column, Label)) <=> (latin(p_1, Column, Label) | latin(p_2, Column, Label)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label)) <=> ![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label)) <=> ![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,axiom,(![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','latin_row_required')).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.43 tff(94,plain,(
% 0.20/0.43 ![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))),
% 0.20/0.43 inference(skolemize,[status(sab)],[93])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | (latin(p_1, p_2, p_2) | latin(p_2, p_2, p_2))) <=> ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | latin(p_1, p_2, p_2) | latin(p_2, p_2, p_2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | (latin(p_1, p_2, p_2) | latin(p_2, p_2, p_2))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | latin(p_1, p_2, p_2) | latin(p_2, p_2, p_2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (latin(p_1, p_2, p_2) | latin(p_2, p_2, p_2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (latin(p_2, p_2, p_2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[99, 75])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (^[Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : refl(((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2)) <=> ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2)) <=> ![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2)) <=> ![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (^[Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~greek(Row1, Column1, Label1)) | (~latin(Row1, Column1, Label2))) | (~greek(Row2, Column2, Label1))) <=> ((~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)))), (((((~greek(Row1, Column1, Label1)) | (~latin(Row1, Column1, Label2))) | (~greek(Row2, Column2, Label1))) | (~latin(Row2, Column2, Label2))) <=> (((~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1))) | (~latin(Row2, Column2, Label2))))), rewrite((((~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1))) | (~latin(Row2, Column2, Label2))) <=> ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)))), (((((~greek(Row1, Column1, Label1)) | (~latin(Row1, Column1, Label2))) | (~greek(Row2, Column2, Label1))) | (~latin(Row2, Column2, Label2))) <=> ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1))))), ((((((~greek(Row1, Column1, Label1)) | (~latin(Row1, Column1, Label2))) | (~greek(Row2, Column2, Label1))) | (~latin(Row2, Column2, Label2))) | eq(Row1, Row2)) <=> (((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1))) | eq(Row1, Row2)))), rewrite((((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1))) | eq(Row1, Row2)) <=> ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))), ((((((~greek(Row1, Column1, Label1)) | (~latin(Row1, Column1, Label2))) | (~greek(Row2, Column2, Label1))) | (~latin(Row2, Column2, Label2))) | eq(Row1, Row2)) <=> ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : (((((~greek(Row1, Column1, Label1)) | (~latin(Row1, Column1, Label2))) | (~greek(Row2, Column2, Label1))) | (~latin(Row2, Column2, Label2))) | eq(Row1, Row2)) <=> ![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.43 tff(106,axiom,(![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : (((((~greek(Row1, Column1, Label1)) | (~latin(Row1, Column1, Label2))) | (~greek(Row2, Column2, Label1))) | (~latin(Row2, Column2, Label2))) | eq(Row1, Row2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','no_two_same2')).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.43 tff(109,plain,(
% 0.20/0.43 ![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))),
% 0.20/0.43 inference(skolemize,[status(sab)],[108])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | (eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (((~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_2)) | eq(p_2, p_1)) <=> (eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_2)) | eq(p_2, p_1))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | (eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_2)) | eq(p_2, p_1))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_2)) | eq(p_2, p_1))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~greek(p_1, p_1, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[116, 110, 41, 100, 88, 87, 26])).
% 0.20/0.43 tff(118,plain,(latin(p_1, p_2, p_2) | (~greek(p_2, p_2, p_2)) | (~greek(p_1, p_1, p_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (latin(p_1, p_2, p_2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[118, 74, 13])).
% 0.20/0.43 tff(120,assumption,(greek(p_1, p_2, p_1)), introduced(assumption)).
% 0.20/0.43 tff(121,assumption,(greek(p_2, p_1, p_1)), introduced(assumption)).
% 0.20/0.43 tff(122,assumption,(latin(p_1, p_2, p_2)), introduced(assumption)).
% 0.20/0.43 tff(123,assumption,(latin(p_2, p_1, p_2)), introduced(assumption)).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | (eq(p_2, p_1) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | (~latin(p_1, p_2, p_2)))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | (~latin(p_1, p_2, p_2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (((~latin(p_1, p_2, p_2)) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | eq(p_2, p_1)) <=> (eq(p_2, p_1) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | (~latin(p_1, p_2, p_2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_2, p_2)) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | eq(p_2, p_1))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | (eq(p_2, p_1) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | (~latin(p_1, p_2, p_2))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[125])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_2, p_2)) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | eq(p_2, p_1))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | (~latin(p_1, p_2, p_2)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[126, 124])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_2, p_2)) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | eq(p_2, p_1))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~greek(p_1, p_2, p_1)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)) | (~latin(p_1, p_2, p_2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[129, 110, 41, 123, 122, 121, 120])).
% 0.20/0.44 tff(131,plain,((~latin(p_2, p_1, p_2)) | (~latin(p_1, p_2, p_2)) | (~greek(p_2, p_1, p_1)) | (~greek(p_1, p_2, p_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (~latin(p_2, p_1, p_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[131, 119, 62, 25])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | (latin(p_1, p_1, p_2) | latin(p_2, p_1, p_2))) <=> ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | latin(p_1, p_1, p_2) | latin(p_2, p_1, p_2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | (latin(p_1, p_1, p_2) | latin(p_2, p_1, p_2))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | latin(p_1, p_1, p_2) | latin(p_2, p_1, p_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (latin(p_1, p_1, p_2) | latin(p_2, p_1, p_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[135, 95])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (latin(p_1, p_1, p_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[136, 132])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | (latin(p_2, p_1, p_2) | latin(p_2, p_2, p_2))) <=> ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | latin(p_2, p_1, p_2) | latin(p_2, p_2, p_2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | (latin(p_2, p_1, p_2) | latin(p_2, p_2, p_2))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | latin(p_2, p_1, p_2) | latin(p_2, p_2, p_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (latin(p_2, p_1, p_2) | latin(p_2, p_2, p_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[140, 82])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (latin(p_2, p_2, p_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[141, 132])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 110, 41, 142, 74, 137, 13])).
% 0.20/0.44 tff(144,plain,(greek(p_1, p_2, p_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(145,assumption,(~greek(p_2, p_1, p_1)), introduced(assumption)).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (greek(p_2, p_1, p_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[61, 145])).
% 0.20/0.44 tff(147,assumption,(latin(p_1, p_1, p_2)), introduced(assumption)).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | (greek(p_2, p_1, p_1) | greek(p_2, p_2, p_1))) <=> ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | greek(p_2, p_1, p_1) | greek(p_2, p_2, p_1))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | (greek(p_2, p_1, p_1) | greek(p_2, p_2, p_1))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | greek(p_2, p_1, p_1) | greek(p_2, p_2, p_1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (greek(p_2, p_1, p_1) | greek(p_2, p_2, p_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[150, 8])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (greek(p_2, p_2, p_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[151, 145])).
% 0.20/0.44 tff(153,assumption,(latin(p_2, p_2, p_2)), introduced(assumption)).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | (eq(p_1, p_2) | (~latin(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~greek(p_1, p_1, p_1)))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_1, p_2) | (~latin(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~greek(p_1, p_1, p_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 (((~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1)) | eq(p_1, p_2)) <=> (eq(p_1, p_2) | (~latin(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~greek(p_1, p_1, p_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1)) | eq(p_1, p_2))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | (eq(p_1, p_2) | (~latin(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~greek(p_1, p_1, p_1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1)) | eq(p_1, p_2))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_1, p_2) | (~latin(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~greek(p_1, p_1, p_1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[156, 154])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1)) | eq(p_1, p_2))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_1, p_2) | (~latin(p_1, p_1, p_2)) | (~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_1)) | (~greek(p_1, p_1, p_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (~greek(p_1, p_1, p_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[159, 37, 110, 153, 152, 147])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | (greek(p_1, p_1, p_1) | greek(p_2, p_1, p_1))) <=> ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | greek(p_1, p_1, p_1) | greek(p_2, p_1, p_1))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | (greek(p_1, p_1, p_1) | greek(p_2, p_1, p_1))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | greek(p_1, p_1, p_1) | greek(p_2, p_1, p_1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[163, 69, 145, 160])).
% 0.20/0.44 tff(165,plain,(greek(p_2, p_1, p_1) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (greek(p_2, p_1, p_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[165, 100, 87])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (^[Label1: $i, Row: $i, Label2: $i, Column: $i] : refl((eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1))) <=> (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1))) <=> ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1))) <=> ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 (^[Label1: $i, Row: $i, Label2: $i, Column: $i] : trans(monotonicity(rewrite(((~greek(Row, Column, Label1)) | (~greek(Row, Column, Label2))) <=> ((~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))), ((((~greek(Row, Column, Label1)) | (~greek(Row, Column, Label2))) | eq(Label1, Label2)) <=> (((~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1))) | eq(Label1, Label2)))), rewrite((((~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1))) | eq(Label1, Label2)) <=> (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))), ((((~greek(Row, Column, Label1)) | (~greek(Row, Column, Label2))) | eq(Label1, Label2)) <=> (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (((~greek(Row, Column, Label1)) | (~greek(Row, Column, Label2))) | eq(Label1, Label2)) <=> ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.45 tff(172,axiom,(![Label1: $i, Row: $i, Label2: $i, Column: $i] : (((~greek(Row, Column, Label1)) | (~greek(Row, Column, Label2))) | eq(Label1, Label2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','greek_element_is_unique')).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.20/0.45 tff(175,plain,(
% 0.20/0.45 ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[174])).
% 0.20/0.45 tff(176,plain,
% 0.20/0.45 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 (((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_1, p_2)))) <=> ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_1, p_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 ((eq(p_1, p_2) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1))) <=> (eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_1, p_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(179,plain,
% 0.20/0.45 (((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_1, p_2) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)))) <=> ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_1, p_2))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[178])).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 (((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_1, p_2) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)))) <=> ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_1, p_2)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[179, 177])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_1, p_2) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_1, p_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[182, 37, 176, 27, 121])).
% 0.20/0.45 tff(184,plain,((~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 (~greek(p_2, p_1, p_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[184, 166])).
% 0.20/0.45 tff(186,plain,
% 0.20/0.45 (((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | (greek(p_2, p_1, p_2) | greek(p_2, p_2, p_2))) <=> ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | greek(p_2, p_1, p_2) | greek(p_2, p_2, p_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | (greek(p_2, p_1, p_2) | greek(p_2, p_2, p_2))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 ((~![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))) | greek(p_2, p_1, p_2) | greek(p_2, p_2, p_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.45 tff(189,plain,
% 0.20/0.45 (greek(p_2, p_1, p_2) | greek(p_2, p_2, p_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[188, 8])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 (greek(p_2, p_2, p_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[189, 185])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 (((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | (greek(p_1, p_1, p_2) | greek(p_2, p_1, p_2))) <=> ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | greek(p_1, p_1, p_2) | greek(p_2, p_1, p_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | (greek(p_1, p_1, p_2) | greek(p_2, p_1, p_2))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(193,plain,
% 0.20/0.45 ((~![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))) | greek(p_1, p_1, p_2) | greek(p_2, p_1, p_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.45 tff(194,plain,
% 0.20/0.45 (greek(p_1, p_1, p_2) | greek(p_2, p_1, p_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[193, 69])).
% 0.20/0.45 tff(195,plain,
% 0.20/0.45 (greek(p_1, p_1, p_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[194, 185])).
% 0.20/0.45 tff(196,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[118, 195, 190, 75])).
% 0.20/0.45 tff(197,plain,(latin(p_1, p_2, p_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(198,plain,
% 0.20/0.45 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | (eq(p_2, p_1) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_1, p_2, p_2)))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_1, p_2, p_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (((~latin(p_1, p_2, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | eq(p_2, p_1)) <=> (eq(p_2, p_1) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_1, p_2, p_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(200,plain,
% 0.20/0.45 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_2, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | eq(p_2, p_1))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | (eq(p_2, p_1) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_1, p_2, p_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[199])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 (((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_2, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | eq(p_2, p_1))) <=> ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_1, p_2, p_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[200, 198])).
% 0.20/0.46 tff(202,plain,
% 0.20/0.46 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | ((~latin(p_1, p_2, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | eq(p_2, p_1))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(203,plain,
% 0.20/0.46 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_2, p_1) | (~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2)) | (~greek(p_1, p_2, p_2)) | (~latin(p_1, p_2, p_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.46 tff(204,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[203, 110, 41, 123, 197, 27, 144])).
% 0.20/0.46 tff(205,plain,((~latin(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(206,plain,
% 0.20/0.46 (~latin(p_2, p_1, p_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[205, 146])).
% 0.20/0.46 tff(207,plain,
% 0.20/0.46 (latin(p_2, p_2, p_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[141, 206])).
% 0.20/0.46 tff(208,plain,
% 0.20/0.46 (latin(p_1, p_1, p_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[136, 206])).
% 0.20/0.46 tff(209,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[165, 208, 207, 145])).
% 0.20/0.46 tff(210,plain,(greek(p_2, p_1, p_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(211,plain,
% 0.20/0.46 (~greek(p_2, p_1, p_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[184, 210])).
% 0.20/0.46 tff(212,plain,
% 0.20/0.46 (greek(p_2, p_2, p_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[189, 211])).
% 0.20/0.46 tff(213,plain,
% 0.20/0.46 (((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | (eq(p_2, p_1) | (~greek(p_2, p_2, p_2)) | (~greek(p_1, p_2, p_2)))) <=> ((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | eq(p_2, p_1) | (~greek(p_2, p_2, p_2)) | (~greek(p_1, p_2, p_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(214,plain,
% 0.20/0.46 ((eq(p_2, p_1) | (~greek(p_1, p_2, p_2)) | (~greek(p_2, p_2, p_2))) <=> (eq(p_2, p_1) | (~greek(p_2, p_2, p_2)) | (~greek(p_1, p_2, p_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(215,plain,
% 0.20/0.46 (((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | (eq(p_2, p_1) | (~greek(p_1, p_2, p_2)) | (~greek(p_2, p_2, p_2)))) <=> ((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | (eq(p_2, p_1) | (~greek(p_2, p_2, p_2)) | (~greek(p_1, p_2, p_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[214])).
% 0.20/0.46 tff(216,plain,
% 0.20/0.46 (((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | (eq(p_2, p_1) | (~greek(p_1, p_2, p_2)) | (~greek(p_2, p_2, p_2)))) <=> ((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | eq(p_2, p_1) | (~greek(p_2, p_2, p_2)) | (~greek(p_1, p_2, p_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[215, 213])).
% 0.20/0.46 tff(217,plain,
% 0.20/0.46 ((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | (eq(p_2, p_1) | (~greek(p_1, p_2, p_2)) | (~greek(p_2, p_2, p_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(218,plain,
% 0.20/0.46 ((~![Row2: $i, Row1: $i, Column: $i, Label: $i] : (eq(Row1, Row2) | (~greek(Row2, Column, Label)) | (~greek(Row1, Column, Label)))) | eq(p_2, p_1) | (~greek(p_2, p_2, p_2)) | (~greek(p_1, p_2, p_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.46 tff(219,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[218, 51, 41, 212, 144])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------