%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC008-1.002 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:17:31 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : MSC008-1.002 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 23:33:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(latin_type, type, (
% 0.12/0.39 latin: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(p_2_type, type, (
% 0.12/0.39 p_2: $i)).
% 0.12/0.39 tff(p_1_type, type, (
% 0.12/0.39 p_1: $i)).
% 0.12/0.39 tff(greek_type, type, (
% 0.12/0.39 greek: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(eq_type, type, (
% 0.12/0.39 eq: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(~latin(p_2, p_1, p_1)), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[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)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,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')).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 ![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | (latin(p_1, p_1, p_1) | latin(p_2, p_1, p_1))) <=> ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | latin(p_1, p_1, p_1) | latin(p_2, p_1, p_1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | (latin(p_1, p_1, p_1) | latin(p_2, p_1, p_1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~![Column: $i, Label: $i] : (latin(p_1, Column, Label) | latin(p_2, Column, Label))) | latin(p_1, p_1, p_1) | latin(p_2, p_1, p_1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (latin(p_1, p_1, p_1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.12/0.39 tff(13,assumption,(~greek(p_2, p_2, p_1)), introduced(assumption)).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (^[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)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.39 tff(19,plain,(
% 0.12/0.39 ![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))),
% 0.12/0.39 inference(skolemize,[status(sab)],[18])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | (greek(p_2, p_2, p_1) | greek(p_2, p_2, p_2))) <=> ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | greek(p_2, p_2, p_1) | greek(p_2, p_2, p_2))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | (greek(p_2, p_2, p_1) | greek(p_2, p_2, p_2))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((~![Row: $i, Column: $i] : (greek(Row, Column, p_1) | greek(Row, Column, p_2))) | greek(p_2, p_2, p_1) | greek(p_2, p_2, p_2)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (greek(p_2, p_2, p_2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[23, 20, 13])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (^[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)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,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')).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,(
% 0.12/0.39 ![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))),
% 0.12/0.39 inference(skolemize,[status(sab)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![Row: $i, Label: $i] : (greek(Row, p_1, Label) | greek(Row, p_2, Label))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (((~![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~![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))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((~![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)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (greek(p_2, p_1, p_1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 31, 13])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (^[Y: $i, X: $i] : refl(((~eq(X, Y)) | eq(Y, X)) <=> ((~eq(X, Y)) | eq(Y, X)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X)) <=> ![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X)) <=> ![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(39,axiom,(![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry')).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.39 tff(41,plain,(
% 0.12/0.39 ![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.12/0.39 inference(skolemize,[status(sab)],[40])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 ((~eq(p_1, p_2)) <=> (~eq(p_1, p_2))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(44,axiom,(~eq(p_1, p_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p_1_is_not_p_2')).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (~eq(p_1, p_2)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (((~![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ((~![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))) | ((~eq(p_2, p_1)) | eq(p_1, p_2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 ((~![Y: $i, X: $i] : ((~eq(X, Y)) | eq(Y, X))) | (~eq(p_2, p_1)) | eq(p_1, p_2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (~eq(p_2, p_1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.40 tff(55,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')).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.12/0.40 tff(58,plain,(
% 0.12/0.40 ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[57])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_2, p_1) | (~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_2, p_1) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 ((eq(p_2, p_1) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_1, p_2))) <=> (eq(p_2, p_1) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_2, p_1) | (~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_2, p_1) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[61])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_2, p_1) | (~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_2, p_1) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[62, 60])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | (eq(p_2, p_1) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_1, p_2)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~greek(Row, Column, Label2)) | (~greek(Row, Column, Label1)))) | eq(p_2, p_1) | (~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 ((~greek(p_2, p_1, p_2)) | (~greek(p_2, p_1, p_1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[65, 59, 49])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (~greek(p_2, p_1, p_2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[66, 35])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (^[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)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(71,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')).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.12/0.40 tff(73,plain,(
% 0.12/0.40 ![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))),
% 0.12/0.40 inference(skolemize,[status(sab)],[72])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (![Column: $i, Label: $i] : (greek(p_1, Column, Label) | greek(p_2, Column, Label))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 ((~![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))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 ((~![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)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (greek(p_1, p_1, p_2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[77, 74, 67])).
% 0.12/0.40 tff(79,assumption,(greek(p_2, p_2, p_2)), introduced(assumption)).
% 0.12/0.40 tff(80,assumption,(greek(p_1, p_1, p_2)), introduced(assumption)).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (^[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)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(84,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')).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.12/0.40 tff(86,plain,(
% 0.12/0.40 ![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))),
% 0.12/0.40 inference(skolemize,[status(sab)],[85])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | (latin(p_2, p_1, p_1) | latin(p_2, p_2, p_1))) <=> ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | latin(p_2, p_1, p_1) | latin(p_2, p_2, p_1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | (latin(p_2, p_1, p_1) | latin(p_2, p_2, p_1))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 ((~![Row: $i, Label: $i] : (latin(Row, p_1, Label) | latin(Row, p_2, Label))) | latin(p_2, p_1, p_1) | latin(p_2, p_2, p_1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (latin(p_2, p_2, p_1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[90, 87, 1])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (^[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)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[92])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[95])).
% 0.12/0.40 tff(97,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')).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.12/0.40 tff(100,plain,(
% 0.12/0.40 ![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))),
% 0.12/0.40 inference(skolemize,[status(sab)],[99])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (((~![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_2, p_2, p_1)) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(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_2, p_2, p_1)) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(103,plain,
% 0.12/0.41 (((~latin(p_2, p_2, p_1)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_2)) | eq(p_1, p_2)) <=> (eq(p_1, p_2) | (~latin(p_2, p_2, p_1)) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(104,plain,
% 0.12/0.41 (((~![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_1)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_2)) | 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_2, p_2, p_1)) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.12/0.41 tff(105,plain,
% 0.12/0.41 (((~![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_1)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_2)) | 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_2, p_2, p_1)) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[104, 102])).
% 0.12/0.41 tff(106,plain,
% 0.12/0.41 ((~![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_1)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_2)) | eq(p_1, p_2))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(107,plain,
% 0.12/0.41 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_1, p_2) | (~latin(p_2, p_2, p_1)) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.12/0.41 tff(108,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[107, 45, 101, 91, 80, 79, 12])).
% 0.12/0.41 tff(109,plain,(latin(p_2, p_1, p_1) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.41 tff(110,plain,
% 0.12/0.41 (latin(p_2, p_1, p_1)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[109, 78, 24])).
% 0.12/0.41 tff(111,plain,
% 0.12/0.41 (^[Label1: $i, Row: $i, Label2: $i, Column: $i] : refl((eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1))) <=> (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(112,plain,
% 0.12/0.41 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1))) <=> ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.12/0.41 tff(113,plain,
% 0.12/0.41 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1))) <=> ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(114,plain,
% 0.12/0.41 (^[Label1: $i, Row: $i, Label2: $i, Column: $i] : trans(monotonicity(rewrite(((~latin(Row, Column, Label1)) | (~latin(Row, Column, Label2))) <=> ((~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))), ((((~latin(Row, Column, Label1)) | (~latin(Row, Column, Label2))) | eq(Label1, Label2)) <=> (((~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1))) | eq(Label1, Label2)))), rewrite((((~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1))) | eq(Label1, Label2)) <=> (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))), ((((~latin(Row, Column, Label1)) | (~latin(Row, Column, Label2))) | eq(Label1, Label2)) <=> (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(115,plain,
% 0.12/0.41 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (((~latin(Row, Column, Label1)) | (~latin(Row, Column, Label2))) | eq(Label1, Label2)) <=> ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[114])).
% 0.12/0.41 tff(116,axiom,(![Label1: $i, Row: $i, Label2: $i, Column: $i] : (((~latin(Row, Column, Label1)) | (~latin(Row, Column, Label2))) | eq(Label1, Label2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','latin_element_is_unique')).
% 0.12/0.41 tff(117,plain,
% 0.12/0.41 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.12/0.41 tff(118,plain,
% 0.12/0.41 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.12/0.41 tff(119,plain,(
% 0.12/0.41 ![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[118])).
% 0.12/0.41 tff(120,plain,
% 0.12/0.41 (![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.12/0.41 tff(121,plain,
% 0.12/0.41 (((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))) | (eq(p_2, p_1) | (~latin(p_2, p_1, p_1)) | (~latin(p_2, p_1, p_2)))) <=> ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))) | eq(p_2, p_1) | (~latin(p_2, p_1, p_1)) | (~latin(p_2, p_1, p_2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(122,plain,
% 0.12/0.41 ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))) | (eq(p_2, p_1) | (~latin(p_2, p_1, p_1)) | (~latin(p_2, p_1, p_2)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(123,plain,
% 0.12/0.41 ((~![Label1: $i, Row: $i, Label2: $i, Column: $i] : (eq(Label1, Label2) | (~latin(Row, Column, Label2)) | (~latin(Row, Column, Label1)))) | eq(p_2, p_1) | (~latin(p_2, p_1, p_1)) | (~latin(p_2, p_1, p_2))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.12/0.41 tff(124,plain,
% 0.12/0.41 ((~latin(p_2, p_1, p_1)) | (~latin(p_2, p_1, p_2))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[123, 120, 49])).
% 0.12/0.41 tff(125,plain,
% 0.12/0.41 (~latin(p_2, p_1, p_2)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[124, 110])).
% 0.12/0.41 tff(126,plain,
% 0.12/0.41 (((~![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))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(127,plain,
% 0.12/0.41 ((~![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))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(128,plain,
% 0.12/0.41 ((~![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)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.12/0.41 tff(129,plain,
% 0.12/0.41 (latin(p_2, p_2, p_2)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[128, 87, 125])).
% 0.12/0.41 tff(130,plain,
% 0.12/0.41 (((~![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))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(131,plain,
% 0.12/0.41 ((~![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))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(132,plain,
% 0.12/0.41 ((~![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)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.12/0.41 tff(133,plain,
% 0.12/0.41 (latin(p_1, p_1, p_2)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[132, 8, 125])).
% 0.12/0.41 tff(134,plain,
% 0.12/0.41 (((~![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) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, 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) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(135,plain,
% 0.12/0.41 (((~latin(p_2, p_2, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_2)) | eq(p_1, p_2)) <=> (eq(p_1, p_2) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(136,plain,
% 0.12/0.41 (((~![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_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_2)) | 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) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[135])).
% 0.12/0.41 tff(137,plain,
% 0.12/0.41 (((~![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_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_2)) | 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) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[136, 134])).
% 0.12/0.41 tff(138,plain,
% 0.12/0.41 ((~![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_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_2)) | eq(p_1, p_2))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(139,plain,
% 0.12/0.41 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_1, p_2) | (~greek(p_1, p_1, p_2)) | (~greek(p_2, p_2, p_2)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.12/0.41 tff(140,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[139, 45, 101, 78, 24, 133, 129])).
% 0.12/0.41 tff(141,plain,(greek(p_2, p_2, p_1)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.41 tff(142,assumption,(greek(p_2, p_1, p_1)), introduced(assumption)).
% 0.12/0.41 tff(143,plain,
% 0.12/0.41 (^[Row: $i, Column2: $i, Label: $i, Column1: $i] : refl((eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label))) <=> (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(144,plain,
% 0.12/0.41 (![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label))) <=> ![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[143])).
% 0.12/0.41 tff(145,plain,
% 0.12/0.41 (![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label))) <=> ![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(146,plain,
% 0.12/0.41 (^[Row: $i, Column2: $i, Label: $i, Column1: $i] : rewrite((((~greek(Row, Column1, Label)) | (~greek(Row, Column2, Label))) | eq(Column1, Column2)) <=> (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(147,plain,
% 0.12/0.41 (![Row: $i, Column2: $i, Label: $i, Column1: $i] : (((~greek(Row, Column1, Label)) | (~greek(Row, Column2, Label))) | eq(Column1, Column2)) <=> ![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[146])).
% 0.12/0.41 tff(148,axiom,(![Row: $i, Column2: $i, Label: $i, Column1: $i] : (((~greek(Row, Column1, Label)) | (~greek(Row, Column2, Label))) | eq(Column1, Column2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','greek_column_is_unique')).
% 0.12/0.41 tff(149,plain,
% 0.12/0.41 (![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.12/0.41 tff(150,plain,
% 0.12/0.41 (![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.12/0.41 tff(151,plain,(
% 0.12/0.41 ![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[150])).
% 0.12/0.41 tff(152,plain,
% 0.12/0.41 (![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.12/0.41 tff(153,plain,
% 0.12/0.41 (((~![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))) | (eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_2, p_1)))) <=> ((~![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))) | eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_2, p_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(154,plain,
% 0.21/0.42 ((eq(p_1, p_2) | (~greek(p_2, p_2, p_1)) | (~greek(p_2, p_1, p_1))) <=> (eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_2, p_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(155,plain,
% 0.21/0.42 (((~![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))) | (eq(p_1, p_2) | (~greek(p_2, p_2, p_1)) | (~greek(p_2, p_1, p_1)))) <=> ((~![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))) | (eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_2, p_1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[154])).
% 0.21/0.42 tff(156,plain,
% 0.21/0.42 (((~![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))) | (eq(p_1, p_2) | (~greek(p_2, p_2, p_1)) | (~greek(p_2, p_1, p_1)))) <=> ((~![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))) | eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_2, p_1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[155, 153])).
% 0.21/0.42 tff(157,plain,
% 0.21/0.42 ((~![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))) | (eq(p_1, p_2) | (~greek(p_2, p_2, p_1)) | (~greek(p_2, p_1, p_1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(158,plain,
% 0.21/0.42 ((~![Row: $i, Column2: $i, Label: $i, Column1: $i] : (eq(Column1, Column2) | (~greek(Row, Column2, Label)) | (~greek(Row, Column1, Label)))) | eq(p_1, p_2) | (~greek(p_2, p_1, p_1)) | (~greek(p_2, p_2, p_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.42 tff(159,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[158, 45, 152, 142, 141])).
% 0.21/0.42 tff(160,plain,(~greek(p_2, p_1, p_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(161,plain,
% 0.21/0.42 (((~![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(162,plain,
% 0.21/0.42 ((~![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))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(163,plain,
% 0.21/0.42 ((~![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)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.42 tff(164,plain,
% 0.21/0.42 (greek(p_1, p_1, p_1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[163, 74, 160])).
% 0.21/0.42 tff(165,plain,
% 0.21/0.42 (((~![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_2, p_2, p_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, 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_2, p_2, p_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(166,plain,
% 0.21/0.42 (((~latin(p_2, p_2, p_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_1)) | eq(p_1, p_2)) <=> (eq(p_1, p_2) | (~latin(p_2, p_2, p_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(167,plain,
% 0.21/0.42 (((~![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_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~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_2, p_2, p_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[166])).
% 0.21/0.42 tff(168,plain,
% 0.21/0.42 (((~![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_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~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_2, p_2, p_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[167, 165])).
% 0.21/0.42 tff(169,plain,
% 0.21/0.42 ((~![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_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_1)) | eq(p_1, p_2))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(170,plain,
% 0.21/0.42 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_1, p_2) | (~latin(p_2, p_2, p_1)) | (~greek(p_2, p_2, p_1)) | (~latin(p_1, p_1, p_1)) | (~greek(p_1, p_1, p_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.42 tff(171,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[170, 45, 101, 91, 141, 164, 12])).
% 0.21/0.42 tff(172,plain,(latin(p_2, p_1, p_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(173,plain,
% 0.21/0.42 (~latin(p_2, p_1, p_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[124, 172])).
% 0.21/0.42 tff(174,plain,
% 0.21/0.42 (latin(p_2, p_2, p_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[128, 87, 173])).
% 0.21/0.42 tff(175,plain,
% 0.21/0.42 (latin(p_1, p_1, p_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[132, 8, 173])).
% 0.21/0.42 tff(176,plain,
% 0.21/0.42 (((~![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) | (~greek(p_2, p_2, p_1)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)) | (~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) | (~greek(p_2, p_2, p_1)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(177,plain,
% 0.21/0.42 (((~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) | (~greek(p_2, p_2, p_1)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(178,plain,
% 0.21/0.42 (((~![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) | (~greek(p_2, p_2, p_1)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[177])).
% 0.21/0.43 tff(179,plain,
% 0.21/0.43 (((~![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_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) | (~greek(p_2, p_2, p_1)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[178, 176])).
% 0.21/0.43 tff(180,plain,
% 0.21/0.43 ((~![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_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))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(181,plain,
% 0.21/0.43 ((~![Row2: $i, Label1: $i, Label2: $i, Column2: $i, Row1: $i, Column1: $i] : ((~latin(Row2, Column2, Label2)) | (~greek(Row2, Column2, Label1)) | (~latin(Row1, Column1, Label2)) | (~greek(Row1, Column1, Label1)) | eq(Row1, Row2))) | eq(p_1, p_2) | (~greek(p_2, p_2, p_1)) | (~latin(p_2, p_2, p_2)) | (~latin(p_1, p_1, p_2)) | (~greek(p_1, p_1, p_1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.21/0.43 tff(182,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[181, 45, 101, 141, 164, 175, 174])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------