%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP050-1 : 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 : n024.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 69.92s 42.23s
% Output : CNFRefutation 70.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 50 ( 39 unt; 0 nHn; 13 RR)
% Number of literals : 63 ( 62 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 19 ( 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 : 142 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X3,
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,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X4)),X2)),multiply(inverse(X4),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(X2),X3)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X2),X2)))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_6,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),X2)),multiply(inverse(X1),X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_2]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(inverse(X4),X2)),multiply(inverse(X4),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4))))))),multiply(X1,X5)) = multiply(inverse(X3),multiply(inverse(multiply(X2,X4)),X5)),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_10,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_11,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4))))),X4)),X5)),X3)),multiply(inverse(X5),multiply(inverse(X5),X5)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4)))))),X6)),X2)),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(X3,multiply(inverse(X4),multiply(inverse(X4),X4))))))),multiply(X1,X5)) = multiply(X3,multiply(inverse(multiply(X2,X4)),X5)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
multiply(X1,inverse(multiply(inverse(X2),X2))) = inverse(multiply(X3,multiply(inverse(multiply(X1,X3)),multiply(inverse(multiply(X1,X3)),multiply(X1,X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_12]),c_0_2]) ).
cnf(c_0_14,plain,
multiply(X1,inverse(multiply(inverse(X2),X2))) = multiply(X1,inverse(multiply(inverse(X3),X3))),
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_15,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,inverse(multiply(inverse(X4),multiply(inverse(multiply(X2,X3)),multiply(inverse(multiply(X5,X3)),multiply(X5,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_16,plain,
inverse(multiply(inverse(X1),X1)) = inverse(multiply(inverse(X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_14]),c_0_2]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X5)),X6)),multiply(inverse(multiply(inverse(multiply(X2,X4)),X5)),X3))),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_18,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_15]) ).
cnf(c_0_19,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_5]) ).
cnf(c_0_20,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(inverse(X2),X2)))) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_8]) ).
cnf(c_0_21,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_22,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,multiply(inverse(X2),X2)))))) = multiply(inverse(X2),X4),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_23,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(inverse(X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_24,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_21,c_0_18]) ).
cnf(c_0_25,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,X4))),multiply(inverse(multiply(X2,X3)),multiply(inverse(multiply(X5,X3)),multiply(X5,X3))))) = X4,
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,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_24,c_0_18]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X4,X2)),multiply(X4,X5))) = multiply(inverse(multiply(X6,X3)),multiply(X6,multiply(X1,X5))),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_29,plain,
inverse(multiply(inverse(X1),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_30,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(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( multiply(multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X1),X1)))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_33,plain,
inverse(multiply(multiply(inverse(X1),X2),X3)) = multiply(inverse(X3),multiply(inverse(X2),X1)),
inference(spm,[status(thm)],[c_0_31,c_0_31]) ).
cnf(c_0_34,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_31]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( multiply(multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X3),X3)))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_36,plain,
multiply(inverse(X1),multiply(inverse(X2),X2)) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_18]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( multiply(multiply(X1,multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),X1)),multiply(inverse(X3),X3))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_35,c_0_18]) ).
cnf(c_0_38,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X4)),multiply(inverse(X3),multiply(inverse(X3),X3)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X5)),X4)),multiply(inverse(X5),multiply(inverse(X5),X5)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_39,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_36]),c_0_31]),c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( multiply(multiply(multiply(inverse(X1),multiply(inverse(X1),X1)),multiply(X1,multiply(inverse(X2),X2))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_10]) ).
cnf(c_0_41,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( multiply(multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),multiply(X1,multiply(inverse(X3),X3))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_43,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_41]),c_0_31]),c_0_34]) ).
cnf(c_0_44,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( multiply(multiply(multiply(inverse(X1),X1),multiply(multiply(inverse(X2),X2),multiply(inverse(X3),X3))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_42,c_0_18]) ).
cnf(c_0_46,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_39]) ).
cnf(c_0_47,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_34]),c_0_34]),c_0_34])]) ).
cnf(c_0_48,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_46]),c_0_39]),c_0_39]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP050-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 13:19:11 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 % start to proof: theBenchmark
% 69.92/42.23 % Version : CSE_E---1.7
% 69.92/42.23 % Problem : theBenchmark.p
% 69.92/42.23 % SZS status Unsatisfiable for theBenchmark.p
% 69.92/42.23 % SZS output start CNFRefutation
% See solution above
% 70.22/42.50 % Total time : 29.390s
%------------------------------------------------------------------------------