%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP059-1 : 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 : n018.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 1.57s 1.81s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of clauses : 34 ( 31 unt; 0 nHn; 5 RR)
% Number of literals : 39 ( 38 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 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 : 76 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2),multiply(X4,inverse(X4)))) = 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(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2),multiply(X4,inverse(X4)))) = X3,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(multiply(multiply(X1,multiply(inverse(multiply(multiply(X2,X3),X1)),X2)),X3),multiply(X4,inverse(X4)))) = multiply(X5,inverse(X5)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),X3),multiply(X4,inverse(X4)))) = inverse(multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),inverse(multiply(X3,inverse(X3))))),X1),X2)) = multiply(X4,inverse(X4)),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
inverse(multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),inverse(X2))) = multiply(X3,inverse(X3)),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_8,plain,
inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X4,inverse(X4)))) = inverse(X3),
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,inverse(X1)),X2)),X3),inverse(X3)),multiply(X4,inverse(X4)))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_10,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(X3,inverse(X3)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_8,c_0_4]) ).
cnf(c_0_11,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X2))))) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
inverse(inverse(multiply(X1,inverse(X1)))) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_11]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(inverse(multiply(X1,inverse(X1)))),X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_14,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_16,plain,
inverse(multiply(X1,multiply(X2,inverse(X2)))) = inverse(X1),
inference(rw,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_14]) ).
cnf(c_0_18,plain,
inverse(multiply(multiply(inverse(X1),X2),inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_15]),c_0_17]) ).
cnf(c_0_19,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_20,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2)) = X3,
inference(rw,[status(thm)],[c_0_2,c_0_16]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(X1,inverse(X1))),X2) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_15]) ).
cnf(c_0_22,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_12]),c_0_19]),c_0_17]) ).
cnf(c_0_23,plain,
inverse(multiply(inverse(multiply(X1,X2)),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,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_26,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_24]),c_0_22]) ).
cnf(c_0_28,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_25,c_0_26])]) ).
cnf(c_0_29,plain,
multiply(inverse(X1),X1) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_4,c_0_22]) ).
cnf(c_0_30,plain,
inverse(multiply(multiply(X1,X2),X3)) = inverse(multiply(X1,multiply(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_30]),c_0_22]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP059-1 : 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
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % 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 18:19:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.57/1.81 % Version : CSE_E---1.7
% 1.57/1.81 % Problem : theBenchmark.p
% 1.57/1.81 % SZS status Unsatisfiable for theBenchmark.p
% 1.57/1.81 % SZS output start CNFRefutation
% See solution above
% 1.57/1.81 % Total time : 1.373s
%------------------------------------------------------------------------------