%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP540-1 : TPTP v9.2.1. Bugfixed v2.7.0.
% 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 : n012.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 04:26:21 PM UTC 2026
% Result : Unsatisfiable 1.12s 1.62s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 4 RR)
% Number of literals : 27 ( 26 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(single_axiom,axiom,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_8,plain,
divide(identity,X1) = inverse(X1),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,axiom,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
single_axiom ).
cnf(c_0_10,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_6]),c_0_8]) ).
cnf(c_0_11,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_12,plain,
divide(X1,divide(divide(divide(X2,X3),X4),divide(divide(X2,X1),X3))) = X4,
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_13,plain,
divide(X1,identity) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_6]),c_0_13]) ).
cnf(c_0_15,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_16,plain,
multiply(divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_6]),c_0_8]),c_0_10]) ).
cnf(c_0_17,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
divide(X1,multiply(identity,X2)) = multiply(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_19,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_6]) ).
cnf(c_0_20,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_17]),c_0_13]),c_0_14]) ).
cnf(c_0_21,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_23,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_10]) ).
cnf(c_0_24,negated_conjecture,
multiply(a,b) != multiply(b,a),
prove_these_axioms_4 ).
cnf(c_0_25,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_22,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
% 0.00/0.06 % Problem : GRP540-1 : TPTP v9.2.1. Bugfixed v2.7.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.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 18:43:15 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.12/1.62 % Version : CSE_E---1.7
% 1.12/1.62 % Problem : theBenchmark.p
% 1.12/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 1.12/1.62 % SZS output start CNFRefutation
% See solution above
% 1.12/1.62 % Total time : 1.362s
%------------------------------------------------------------------------------