%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP085-1 : TPTP v9.2.1. Bugfixed v2.7.0.
% 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 : n006.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 04:23:45 PM UTC 2026
% Result : Unsatisfiable 1.40s 1.77s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of clauses : 28 ( 24 unt; 0 nHn; 7 RR)
% Number of literals : 37 ( 36 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))) = X2,
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))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))) = X2,
single_axiom ).
cnf(c_0_3,plain,
multiply(multiply(X1,X2),inverse(multiply(multiply(multiply(X3,X1),X4),X2))) = inverse(multiply(X3,X4)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(multiply(X1,inverse(multiply(X2,X3))),inverse(X1)) = inverse(multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_5,plain,
multiply(multiply(X1,inverse(X2)),inverse(X1)) = inverse(X2),
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_6,plain,
multiply(X1,inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X3))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_7,plain,
multiply(inverse(X1),inverse(multiply(X2,inverse(X1)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,plain,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
inverse(inverse(inverse(X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_11,plain,
inverse(multiply(X1,inverse(X2))) = multiply(inverse(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_10]) ).
cnf(c_0_12,plain,
multiply(multiply(X1,X2),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_13,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_14,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))
| multiply(a4,b4) != multiply(b4,a4) ),
prove_these_axioms ).
cnf(c_0_15,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(a2,multiply(b2,inverse(b2))) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_15]),c_0_15]),c_0_15]),c_0_15])]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_12]),c_0_11]),c_0_15]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_21,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_2]),c_0_10]) ).
cnf(c_0_23,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(sr,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_22]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP085-1 : TPTP v9.2.1. Bugfixed v2.7.0.
% 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 : n006.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 18:20:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.40/1.77 % Version : CSE_E---1.7
% 1.40/1.77 % Problem : theBenchmark.p
% 1.40/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.40/1.77 % SZS output start CNFRefutation
% See solution above
% 1.40/1.77 % Total time : 1.373s
%------------------------------------------------------------------------------