%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP446-1 : 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 : 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 04:26:08 PM UTC 2026
% Result : Unsatisfiable 1.20s 1.68s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 4 RR)
% Number of literals : 27 ( 26 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c_0_4,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
divide(inverse(divide(X1,X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
single_axiom ).
cnf(c_0_9,plain,
multiply(inverse(divide(X1,X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
divide(multiply(inverse(X1),X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_11,plain,
divide(X1,divide(divide(inverse(X2),X3),divide(inverse(X1),X3))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_5]),c_0_5]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_13,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_5]),c_0_6]),c_0_6]) ).
cnf(c_0_15,plain,
multiply(inverse(inverse(inverse(multiply(inverse(X1),X1)))),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_16,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_18,plain,
multiply(X1,inverse(inverse(inverse(X2)))) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_6,c_0_16]) ).
cnf(c_0_19,plain,
inverse(multiply(divide(inverse(X1),X2),X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_11]),c_0_7]),c_0_6]) ).
cnf(c_0_20,plain,
divide(inverse(inverse(X1)),X2) = divide(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_21,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
prove_these_axioms_2 ).
cnf(c_0_22,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_23,plain,
inverse(multiply(divide(X1,X2),X2)) = inverse(X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
inverse(inverse(a2)) != a2,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP446-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.09 % 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
% 0.11/0.29 % Computer : n006.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Mon May 4 18:36:01 EDT 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.30 % start to proof: theBenchmark
% 1.20/1.68 % Version : CSE_E---1.7
% 1.20/1.68 % Problem : theBenchmark.p
% 1.20/1.68 % SZS status Unsatisfiable for theBenchmark.p
% 1.20/1.68 % SZS output start CNFRefutation
% See solution above
% 1.20/1.68 % Total time : 1.369s
%------------------------------------------------------------------------------