%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG007-4 : 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 05:04:58 PM UTC 2026
% Result : Unsatisfiable 1.12s 1.86s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 3 RR)
% Number of literals : 21 ( 20 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 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 : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply_additive_inverse1,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).
cnf(boolean_ring,hypothesis,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
cnf(multiply_additive_inverse2,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).
cnf(left_additive_inverse,axiom,
add(additive_inverse(X1),X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).
cnf(commutative_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
cnf(prove_inverse,negated_conjecture,
add(a,a) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse) ).
cnf(c_0_7,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse1 ).
cnf(c_0_8,hypothesis,
multiply(X1,X1) = X1,
boolean_ring ).
cnf(c_0_9,hypothesis,
multiply(X1,additive_inverse(X1)) = additive_inverse(X1),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_11,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse2 ).
cnf(c_0_12,axiom,
add(additive_inverse(X1),X1) = additive_identity,
left_additive_inverse ).
cnf(c_0_13,axiom,
add(X1,X2) = add(X2,X1),
commutative_addition ).
cnf(c_0_14,hypothesis,
multiply(additive_inverse(X1),X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_16,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,hypothesis,
additive_inverse(X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_9]) ).
cnf(c_0_18,negated_conjecture,
add(a,a) != additive_identity,
prove_inverse ).
cnf(c_0_19,plain,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.20 % Problem : RNG007-4 : TPTP v9.2.1. Released v1.0.0.
% 0.02/0.20 % 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
% 0.12/0.44 % Computer : n022.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8042.1875MB
% 0.12/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Tue May 5 01:45:51 EDT 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.45 % start to proof: theBenchmark
% 1.12/1.86 % Version : CSE_E---1.7
% 1.12/1.86 % Problem : theBenchmark.p
% 1.12/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.12/1.86 % SZS output start CNFRefutation
% See solution above
% 1.12/1.86 % Total time : 1.399s
%------------------------------------------------------------------------------