%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP451-1 : TPTP v9.2.1. Released v2.6.0.
% 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 : n027.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 04:26:09 PM UTC 2026
% Result : Unsatisfiable 1.23s 1.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 3 RR)
% Number of literals : 24 ( 23 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(divide(X1,X1),divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_4,axiom,
divide(divide(divide(X1,X1),divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),X3) = X2,
single_axiom ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_7,plain,
divide(inverse(divide(X1,divide(X2,divide(inverse(X1),X3)))),X3) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_5]),c_0_5]) ).
cnf(c_0_8,plain,
divide(inverse(divide(X1,X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_9,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_10,plain,
divide(inverse(inverse(multiply(X1,X2))),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_5]) ).
cnf(c_0_11,plain,
multiply(inverse(inverse(multiply(X1,inverse(X2)))),X2) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_5,c_0_9]) ).
cnf(c_0_13,plain,
inverse(inverse(multiply(X1,inverse(inverse(X2))))) = multiply(inverse(inverse(X1)),X2),
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
cnf(c_0_14,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_15,plain,
multiply(multiply(inverse(inverse(X1)),X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_13]),c_0_9]) ).
cnf(c_0_16,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
multiply(multiply(X1,X2),inverse(X2)) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
multiply(X1,inverse(inverse(inverse(X2)))) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_19,plain,
multiply(divide(X1,X2),X2) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]) ).
cnf(c_0_20,plain,
divide(inverse(inverse(divide(X1,X1))),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_21,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
prove_these_axioms_1 ).
cnf(c_0_22,plain,
multiply(inverse(X1),X1) = divide(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP451-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.11 % 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 : n027.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
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:36:05 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.23/1.71 % SZS output start CNFRefutation
% See solution above
% 1.23/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------