%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG011-5 : 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 : n022.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 05:04:59 PM UTC 2026
% Result : Unsatisfiable 0.28s 1.62s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 4 RR)
% Number of literals : 12 ( 11 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(middle_associator,axiom,
multiply(multiply(associator(X1,X1,X2),X1),associator(X1,X1,X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',middle_associator) ).
cnf(associator,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
cnf(prove_equality,negated_conjecture,
multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality) ).
cnf(multiply_additive_inverse1,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse1) ).
cnf(c_0_4,axiom,
multiply(multiply(associator(X1,X1,X2),X1),associator(X1,X1,X2)) = additive_identity,
middle_associator ).
cnf(c_0_5,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_6,negated_conjecture,
multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity,
prove_equality ).
cnf(c_0_7,plain,
multiply(multiply(add(multiply(multiply(X1,X1),X2),additive_inverse(multiply(X1,multiply(X1,X2)))),X1),add(multiply(multiply(X1,X1),X2),additive_inverse(multiply(X1,multiply(X1,X2))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_5]),c_0_5]) ).
cnf(c_0_8,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse1 ).
cnf(c_0_9,negated_conjecture,
multiply(multiply(add(multiply(multiply(a,a),b),additive_inverse(multiply(a,multiply(a,b)))),a),add(multiply(multiply(a,a),b),additive_inverse(multiply(a,multiply(a,b))))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_5]),c_0_5]) ).
cnf(c_0_10,plain,
multiply(multiply(add(multiply(multiply(X1,X1),X2),multiply(X1,multiply(X1,additive_inverse(X2)))),X1),add(multiply(multiply(X1,X1),X2),multiply(X1,multiply(X1,additive_inverse(X2))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]),c_0_8]),c_0_8]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_8]),c_0_8]),c_0_8]),c_0_8]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG011-5 : 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
% 0.16/0.33 % Computer : n022.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 : Tue May 5 01:48:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.28/1.62 % Version : CSE_E---1.7
% 0.28/1.62 % Problem : theBenchmark.p
% 0.28/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.28/1.62 % SZS output start CNFRefutation
% See solution above
% 0.28/1.62 % Total time : 1.272s
%------------------------------------------------------------------------------