%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM025-2 : 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 : n011.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 04:52:45 PM UTC 2026
% Result : Unsatisfiable 0.29s 1.63s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of clauses : 33 ( 19 unt; 4 nHn; 17 RR)
% Number of literals : 51 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_lemma,axiom,
( greater_or_equalish(X1,X2)
| equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_lemma) ).
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(smaller_number,axiom,
( ~ equalish(add(successor(X1),X2),X3)
| ~ greater_or_equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,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(transitivity_of_less,axiom,
( greater_or_equalish(X1,X2)
| greater_or_equalish(X3,X1)
| ~ greater_or_equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
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(symmetry,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
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,axiom,
~ equalish(successor(X1),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_the_first_number) ).
cnf(prove_b_not_less_than_a,negated_conjecture,
~ greater_or_equalish(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_not_less_than_a) ).
cnf(a_less_than_b,hypothesis,
~ greater_or_equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_less_than_b) ).
cnf(no_number_less_than_itself,axiom,
greater_or_equalish(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_number_less_than_itself) ).
cnf(reflexivity,axiom,
equalish(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
cnf(i_0_16,axiom,
( greater_or_equalish(X1,X2)
| equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2) ),
less_lemma,
[final] ).
cnf(i_0_17,axiom,
equalish(multiply(X1,successor(X2)),add(multiply(X1,X2),X1)),
times,
[final] ).
cnf(i_0_18,axiom,
equalish(add(X1,successor(X2)),successor(add(X1,X2))),
addition,
[final] ).
cnf(i_0_19,axiom,
( ~ equalish(add(successor(X1),X2),X3)
| ~ greater_or_equalish(X2,X3) ),
smaller_number,
[final] ).
cnf(i_0_20,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity,
[final] ).
cnf(i_0_21,axiom,
( equalish(X1,X2)
| ~ equalish(successor(X1),successor(X2)) ),
successor_equality1,
[final] ).
cnf(i_0_22,axiom,
( greater_or_equalish(X1,X2)
| greater_or_equalish(X3,X1)
| ~ greater_or_equalish(X3,X2) ),
transitivity_of_less,
[final] ).
cnf(i_0_23,axiom,
( equalish(successor(X1),successor(X2))
| ~ equalish(X1,X2) ),
successor_substitution,
[final] ).
cnf(i_0_24,axiom,
equalish(add(X1,n0),X1),
adding_zero,
[final] ).
cnf(i_0_25,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetry,
[final] ).
cnf(i_0_26,axiom,
equalish(multiply(X1,n0),n0),
times_zero,
[final] ).
cnf(i_0_27,axiom,
~ equalish(successor(X1),n0),
zero_is_the_first_number,
[final] ).
cnf(i_0_28,negated_conjecture,
~ greater_or_equalish(b,a),
prove_b_not_less_than_a,
[final] ).
cnf(i_0_29,hypothesis,
~ greater_or_equalish(a,b),
a_less_than_b,
[final] ).
cnf(i_0_30,axiom,
greater_or_equalish(X1,X1),
no_number_less_than_itself,
[final] ).
cnf(i_0_31,axiom,
equalish(X1,X1),
reflexivity,
[final] ).
cnf(i_0_32,plain,
$false,
inference(scs_inference,[],[i_0_28,i_0_29,i_0_30,i_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM025-2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.00/0.13 % 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
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 00:06:17 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.29/1.63 % Version : CSE_E---1.7
% 0.29/1.63 % Problem : theBenchmark.p
% 0.29/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 0.29/1.63 % SZS output start CNFRefutation
% See solution above
% 0.29/1.65 % Total time : 1.275s
%------------------------------------------------------------------------------