%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM025-2 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:18:33 PM UTC 2026
% Result : Unsatisfiable 6.17s 1.24s
% Output : Proof 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 38 unt; 0 def)
% Number of atoms : 58 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 26 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 54 ( 6 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
( ~ greater_or_equalish(C,B)
| greater_or_equalish(C,A)
| greater_or_equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f9_nnf,plain,
! [A,B,C] :
( ~ greater_or_equalish(C,B)
| greater_or_equalish(C,A)
| greater_or_equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C] :
( ~ greater_or_equalish(C,B)
| greater_or_equalish(C,A)
| greater_or_equalish(A,B) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ greater_or_equalish(X2,X1)
| greater_or_equalish(X2,X0)
| greater_or_equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t25,plain,
ifeq(greater_or_equalish(X1,X2),true,or(greater_or_equalish(X3,X2),greater_or_equalish(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t76,plain,
ifeq(greater_or_equalish(X1,X2),true,or(greater_or_equalish(X3,X2),greater_or_equalish(X1,X3)),true) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(f13,axiom,
greater_or_equalish(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_number_less_than_itself) ).
fof(f13_nnf,plain,
! [A] : greater_or_equalish(A,A),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] : greater_or_equalish(A,A),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
greater_or_equalish(X0,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t3,plain,
greater_or_equalish(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t81,plain,
greater_or_equalish(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t82,plain,
true = ifeq(true,true,or(greater_or_equalish(X1,X2),greater_or_equalish(X2,X1)),true),
inference(cp,[status(thm)],[t76,t81]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t178,plain,
true = or(greater_or_equalish(X1,X2),greater_or_equalish(X2,X1)),
inference(step,[status(thm)],[t82,t28]) ).
cnf(t153,plain,
or(greater_or_equalish(X1,X2),greater_or_equalish(X2,X1)) = true,
inference(orient,[status(thm)],[t178]) ).
cnf(f15,negated_conjecture,
~ greater_or_equalish(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_not_less_than_a) ).
fof(f15_nnf,plain,
~ greater_or_equalish(b,a),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ greater_or_equalish(b,a),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ greater_or_equalish(b,a),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t5,plain,
greater_or_equalish(b,a) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t112,plain,
greater_or_equalish(b,a) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t154,plain,
true = or(false,greater_or_equalish(a,b)),
inference(cp,[status(thm)],[t153,t112]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t30,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t179,plain,
true = greater_or_equalish(a,b),
inference(step,[status(thm)],[t154,t30]) ).
cnf(f14,hypothesis,
~ greater_or_equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_less_than_b) ).
fof(f14_nnf,plain,
~ greater_or_equalish(a,b),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ greater_or_equalish(a,b),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ greater_or_equalish(a,b),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t4,plain,
greater_or_equalish(a,b) = false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t105,plain,
greater_or_equalish(a,b) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t180,plain,
true = false,
inference(step,[status(thm)],[t179,t105]) ).
cnf(t158,plain,
false = true,
inference(orient,[status(thm)],[t180]) ).
cnf(f10,axiom,
( ~ greater_or_equalish(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).
fof(f10_nnf,plain,
! [A,B,C] :
( ~ greater_or_equalish(B,C)
| ~ equalish(add(successor(A),B),C) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B,C] :
( ~ greater_or_equalish(B,C)
| ~ equalish(add(successor(A),B),C) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ greater_or_equalish(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f12,axiom,
~ equalish(successor(A),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_the_first_number) ).
fof(f12_nnf,plain,
! [A] : ~ equalish(successor(A),n0),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : ~ equalish(successor(A),n0),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ equalish(successor(X0),n0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10,c12,c14,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t158]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM025-2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 02:42:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.17/1.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/1.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------