%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP053-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 : Tue May 5 04:23:41 PM UTC 2026
% Result : Unsatisfiable 95.80s 57.00s
% Output : CNFRefutation 96.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 52 ( 45 unt; 0 nHn; 9 RR)
% Number of literals : 61 ( 60 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1)))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1)))))) = X3,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3))),inverse(multiply(inverse(X1),X1)))))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(X3)))),inverse(multiply(inverse(X4),X4))))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))),inverse(multiply(inverse(X1),X1))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),X3)),inverse(multiply(inverse(X1),X1)))))) = multiply(inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,inverse(inverse(X3))))),inverse(multiply(inverse(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_4]) ).
cnf(c_0_6,plain,
multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(inverse(X2),X2)))))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_2]) ).
cnf(c_0_7,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3))),inverse(multiply(inverse(X1),X1))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X3))))))),inverse(multiply(inverse(X2),X2))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_5]) ).
cnf(c_0_9,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X4)))),inverse(multiply(inverse(inverse(multiply(X2,X3))),inverse(multiply(X2,X3)))))) = multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(X4,inverse(multiply(inverse(X3),X3)))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_3]),c_0_7]) ).
cnf(c_0_10,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(inverse(multiply(X3,inverse(X4))))))),X1)),X4)),inverse(multiply(inverse(X1),X1)))))) = multiply(inverse(X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_8]),c_0_4]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X3))),inverse(multiply(inverse(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_3]),c_0_2]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2))))))))) = X3,
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))) = multiply(inverse(X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_8]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X3),X3),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X2),X2)))),inverse(multiply(inverse(multiply(X3,multiply(X2,inverse(X4)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X2),X2)))))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_16,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(inverse(X1)),inverse(X1))))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_8]),c_0_8]),c_0_8]) ).
cnf(c_0_18,plain,
inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3)))))) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_19,plain,
inverse(multiply(inverse(X1),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_18]),c_0_18]) ).
cnf(c_0_20,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_21,plain,
inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),X2)))) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X1),X1))))))) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_23,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X3))))) = X3,
inference(rw,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_24,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3))))))) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_25,plain,
multiply(inverse(inverse(inverse(multiply(X1,X2)))),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_26,plain,
inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
inverse(inverse(multiply(X1,multiply(inverse(X2),X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_18]),c_0_18]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(inverse(X1),X1)),inverse(X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(X2),X2))))) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_30,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
prove_these_axioms ).
cnf(c_0_32,plain,
multiply(inverse(X1),inverse(inverse(multiply(X1,X2)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_30]) ).
cnf(c_0_33,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_34,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(sr,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_35,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_32]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(X1),X1),a2) != a2 ),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_37,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X2),X2)))))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_9]) ).
cnf(c_0_38,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_39,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( multiply(multiply(X1,multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(X1,inverse(multiply(inverse(X3),X3)))))))))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(X5)))),inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X1),X1)))))) = multiply(X6,inverse(multiply(inverse(multiply(inverse(multiply(X7,X6)),multiply(X7,X5))),inverse(multiply(inverse(X6),X6))))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_42,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( multiply(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),multiply(inverse(multiply(X4,X2)),multiply(X4,X3))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_7]),c_0_2]) ).
cnf(c_0_44,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_45,plain,
multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(X2,X3))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_21]),c_0_35]) ).
cnf(c_0_46,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_42,c_0_35]) ).
cnf(c_0_47,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(multiply(inverse(X1),X1)),a2) != a2 ),
inference(spm,[status(thm)],[c_0_43,c_0_20]) ).
cnf(c_0_48,plain,
multiply(multiply(X1,inverse(X2)),multiply(X2,X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_30])]) ).
cnf(c_0_50,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_39]),c_0_35]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP053-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:19:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 95.80/57.00 % Version : CSE_E---1.7
% 95.80/57.00 % Problem : theBenchmark.p
% 95.80/57.00 % SZS status Unsatisfiable for theBenchmark.p
% 95.80/57.00 % SZS output start CNFRefutation
% See solution above
% 96.20/57.37 % Total time : 40.464s
%------------------------------------------------------------------------------