%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM020-1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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 : n024.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 04:52:44 PM UTC 2026
% Result : Unsatisfiable 1.17s 1.63s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 7 unt; 0 nHn; 9 RR)
% Number of literals : 22 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(successor_substitution,axiom,
( equalish(successor(X1),successor(X2))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',successor_substitution) ).
cnf(addition,axiom,
equalish(add(X1,successor(X2)),successor(add(X1,X2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',addition) ).
cnf(deny_addition_lemma,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deny_addition_lemma) ).
cnf(adding_zero,axiom,
equalish(add(X1,n0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',adding_zero) ).
cnf(c_0_5,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity ).
cnf(c_0_6,axiom,
( equalish(successor(X1),successor(X2))
| ~ equalish(X1,X2) ),
successor_substitution ).
cnf(c_0_7,plain,
( equalish(X1,successor(X2))
| ~ equalish(X1,successor(X3))
| ~ equalish(X3,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
equalish(add(X1,successor(X2)),successor(add(X1,X2))),
addition ).
cnf(c_0_9,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)),
deny_addition_lemma ).
cnf(c_0_10,plain,
( equalish(add(X1,successor(X2)),successor(X3))
| ~ equalish(add(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
equalish(add(X1,n0),X1),
adding_zero ).
cnf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM020-1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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 : n024.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 19:05:41 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 % start to proof: theBenchmark
% 1.17/1.63 % Version : CSE_E---1.7
% 1.17/1.63 % Problem : theBenchmark.p
% 1.17/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 1.17/1.63 % SZS output start CNFRefutation
% See solution above
% 1.17/1.63 % Total time : 1.360s
%------------------------------------------------------------------------------