%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP062-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 04:23:42 PM UTC 2026
% Result : Unsatisfiable 4.05s 3.26s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 2
% Syntax : Number of clauses : 61 ( 58 unt; 0 nHn; 5 RR)
% Number of literals : 66 ( 65 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 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 : 173 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2))))))) = X4,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2))))))) = X4,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,X1)))),multiply(multiply(X5,inverse(X5)),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X4)))),multiply(multiply(multiply(X5,inverse(X5)),X2),multiply(multiply(X6,inverse(X6)),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(multiply(multiply(X3,inverse(X3)),X4),multiply(multiply(X5,inverse(X5)),X6)))) = multiply(multiply(X7,inverse(X7)),inverse(multiply(X2,multiply(X4,X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,X4))),multiply(X2,X3)))) = X4,
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
multiply(multiply(X1,inverse(X1)),X2) = multiply(multiply(X3,inverse(X3)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_4]),c_0_3]) ).
cnf(c_0_8,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_7]),c_0_2]) ).
cnf(c_0_9,plain,
inverse(multiply(X1,multiply(inverse(X1),multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,inverse(X4)))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_10,plain,
inverse(multiply(X1,multiply(inverse(X1),X2))) = inverse(multiply(X3,multiply(inverse(X3),X2))),
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_11,plain,
inverse(multiply(inverse(X1),multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(inverse(X4),X2))))))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_10]) ).
cnf(c_0_12,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),multiply(X4,inverse(X4))))) = X3,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(X1),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3))) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
inverse(multiply(inverse(inverse(inverse(multiply(X1,multiply(inverse(X1),X2))))),multiply(X2,multiply(multiply(X3,inverse(X3)),X4)))) = inverse(X4),
inference(spm,[status(thm)],[c_0_2,c_0_13]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,inverse(X3)))),multiply(X2,X4)))) = inverse(X4),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_16,plain,
inverse(inverse(multiply(X1,multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3)))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_14]) ).
cnf(c_0_17,plain,
multiply(multiply(X1,inverse(X1)),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),multiply(X4,inverse(X4)))) = inverse(X3),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_18,plain,
inverse(inverse(inverse(multiply(X1,inverse(X1))))) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_11]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(X1)) = multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X3,inverse(X3))),
inference(spm,[status(thm)],[c_0_8,c_0_18]) ).
cnf(c_0_21,plain,
multiply(X1,inverse(X1)) = multiply(X2,multiply(inverse(X2),inverse(inverse(inverse(inverse(multiply(X3,inverse(X3)))))))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
multiply(inverse(X1),inverse(inverse(inverse(inverse(multiply(X2,inverse(X2))))))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_21]),c_0_15]) ).
cnf(c_0_23,plain,
multiply(inverse(X1),inverse(multiply(X2,inverse(X2)))) = inverse(X1),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_4]) ).
cnf(c_0_25,plain,
inverse(multiply(inverse(X1),inverse(inverse(inverse(multiply(X2,inverse(X2))))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_24]),c_0_23]) ).
cnf(c_0_26,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,inverse(X3)))),multiply(X4,inverse(X4))))) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_27,plain,
inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(inverse(inverse(multiply(X2,inverse(X2)))))) = multiply(X3,multiply(inverse(X3),inverse(inverse(X1)))),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,inverse(X1)),multiply(X2,multiply(X3,inverse(X3)))) = inverse(inverse(X2)),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
inverse(multiply(X1,multiply(inverse(X1),inverse(inverse(inverse(X2)))))) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_31,plain,
inverse(inverse(inverse(inverse(inverse(multiply(X1,multiply(inverse(X1),X2))))))) = inverse(X2),
inference(rw,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_32,plain,
inverse(inverse(inverse(inverse(multiply(X1,multiply(inverse(X1),X2)))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_30]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,inverse(X1)),multiply(X2,multiply(inverse(X2),X3))) = X3,
inference(rw,[status(thm)],[c_0_12,c_0_27]) ).
cnf(c_0_34,plain,
inverse(multiply(X1,multiply(inverse(X1),inverse(inverse(X2))))) = inverse(multiply(X2,multiply(X3,inverse(X3)))),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),X3))) = multiply(X4,multiply(inverse(X4),multiply(inverse(inverse(X1)),X3))),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_36,plain,
multiply(inverse(inverse(multiply(X1,inverse(X1)))),X2) = inverse(inverse(inverse(inverse(X2)))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))) = multiply(X2,multiply(X3,inverse(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_34]),c_0_11]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(inverse(inverse(X2)))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33]) ).
cnf(c_0_39,plain,
multiply(inverse(inverse(X1)),multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(multiply(X3,multiply(X4,multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,multiply(X3,X4)))))),X6),inverse(multiply(X7,multiply(X1,X2))))))) = X7,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_41,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_18]),c_0_36]),c_0_22]) ).
cnf(c_0_42,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(multiply(multiply(multiply(X3,inverse(X3)),X4),multiply(multiply(multiply(X5,inverse(X5)),X6),multiply(multiply(X7,inverse(X7)),X8))),multiply(multiply(X9,inverse(X9)),inverse(multiply(X4,multiply(X6,X8))))),inverse(multiply(X10,multiply(X1,X2))))))) = X10,
inference(spm,[status(thm)],[c_0_40,c_0_4]) ).
cnf(c_0_43,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_41]),c_0_41]),c_0_41]) ).
cnf(c_0_44,plain,
inverse(multiply(X1,multiply(X2,inverse(multiply(X3,multiply(X1,X2)))))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_43]),c_0_43]),c_0_43]),c_0_43]) ).
cnf(c_0_45,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
cnf(c_0_46,plain,
inverse(multiply(X1,inverse(multiply(X2,X1)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_45]) ).
cnf(c_0_47,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_41]),c_0_41]) ).
cnf(c_0_48,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_41,c_0_46]) ).
cnf(c_0_49,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_50,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_41]) ).
cnf(c_0_51,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_41]) ).
cnf(c_0_52,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_48]),c_0_41]) ).
cnf(c_0_53,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_54,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_45])]) ).
cnf(c_0_56,plain,
multiply(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_8,c_0_41]) ).
cnf(c_0_57,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_43]),c_0_54]) ).
cnf(c_0_58,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_56]) ).
cnf(c_0_59,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_57]),c_0_41]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP062-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:17:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.19/0.34 % start to proof: theBenchmark
% 4.05/3.26 % Version : CSE_E---1.7
% 4.05/3.26 % Problem : theBenchmark.p
% 4.05/3.26 % SZS status Unsatisfiable for theBenchmark.p
% 4.05/3.26 % SZS output start CNFRefutation
% See solution above
% 4.05/3.27 % Total time : 2.370s
%------------------------------------------------------------------------------