%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM019-1 : 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 : n014.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 0.26s 1.61s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 17 unt; 0 nHn; 13 RR)
% Number of literals : 31 ( 0 equ; 12 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(times,axiom,
equalish(multiply(X1,successor(X2)),add(multiply(X1,X2),X1)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',times) ).
cnf(addition,axiom,
equalish(add(X1,successor(X2)),successor(add(X1,X2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',addition) ).
cnf(transitivity,hypothesis,
( equalish(X2,X3)
| ~ equalish(X1,X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(successor_equality1,axiom,
( equalish(X1,X2)
| ~ equalish(successor(X1),successor(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',successor_equality1) ).
cnf(successor_substitution,axiom,
( equalish(successor(X1),successor(X2))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',successor_substitution) ).
cnf(adding_zero,axiom,
equalish(add(X1,n0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',adding_zero) ).
cnf(times_zero,axiom,
equalish(multiply(X1,n0),n0),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',times_zero) ).
cnf(zero_is_the_first_number,hypothesis,
~ equalish(successor(X1),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_the_first_number) ).
cnf(prove_b_equals_a,negated_conjecture,
~ equalish(aa,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_a) ).
cnf(reflexivity,hypothesis,
equalish(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
cnf(a_equals_aa,hypothesis,
equalish(a,aa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_aa) ).
cnf(i_0_11,axiom,
equalish(multiply(X1,successor(X2)),add(multiply(X1,X2),X1)),
times,
[final] ).
cnf(i_0_12,axiom,
equalish(add(X1,successor(X2)),successor(add(X1,X2))),
addition,
[final] ).
cnf(i_0_13,hypothesis,
( equalish(X2,X3)
| ~ equalish(X1,X2)
| ~ equalish(X1,X3) ),
transitivity,
[final] ).
cnf(i_0_14,axiom,
( equalish(X1,X2)
| ~ equalish(successor(X1),successor(X2)) ),
successor_equality1,
[final] ).
cnf(i_0_15,axiom,
( equalish(successor(X1),successor(X2))
| ~ equalish(X1,X2) ),
successor_substitution,
[final] ).
cnf(i_0_16,axiom,
equalish(add(X1,n0),X1),
adding_zero,
[final] ).
cnf(i_0_17,axiom,
equalish(multiply(X1,n0),n0),
times_zero,
[final] ).
cnf(i_0_18,hypothesis,
~ equalish(successor(X1),n0),
zero_is_the_first_number,
[final] ).
cnf(i_0_19,negated_conjecture,
~ equalish(aa,a),
prove_b_equals_a,
[final] ).
cnf(i_0_20,hypothesis,
equalish(X1,X1),
reflexivity,
[final] ).
cnf(i_0_21,hypothesis,
equalish(a,aa),
a_equals_aa,
[final] ).
cnf(i_0_22,plain,
$false,
inference(scs_inference,[],[i_0_19,i_0_20,i_0_21,i_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM019-1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:06:06 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.26/1.61 % Version : CSE_E---1.7
% 0.26/1.61 % Problem : theBenchmark.p
% 0.26/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.26/1.61 % SZS output start CNFRefutation
% See solution above
% 0.26/1.62 % Total time : 1.270s
%------------------------------------------------------------------------------