%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 : Sun Sep 27 08:10:10 AM UTC 2026
% Result : Theorem 7.90s 3.83s
% Output : Refutation 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 56
% Syntax : Number of formulae : 114 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 235 ( 116 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 921 ( 42 ~; 30 |; 24 &; 758 @)
% ( 4 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 249 ( 0 ^; 231 !; 18 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
thf(vmul_decl,type,
vmul: $i > $i > $i ).
thf(vd448_decl,type,
vd448: $i ).
thf(vd449_decl,type,
vd449: $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(v1_decl,type,
v1: $i ).
thf(vskolem2_decl,type,
vskolem2: $i > $i ).
thf(18,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(120,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(54,axiom,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( A @ vsucc @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( vd449 @ ( vd448 @ vmul ) @ ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 3)') ).
thf(257,plain,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( A @ vsucc @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( vd449 @ ( vd448 @ vmul ) @ ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ greater ) )
& ( D @ ( C @ greater ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ greater ) )
& ( D @ ( C @ greater ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(117,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(38,axiom,
! [A: $i] : ( v1 @ ( A @ geq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
thf(197,plain,
! [A: $i] : ( v1 @ ( A @ geq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(173,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(266,plain,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( vd449 @ ( vd448 @ vmul ) @ ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) @ vplus ) )
= ( vd449 @ ( vd448 @ vmul ) @ ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 2)') ).
thf(204,plain,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( vd449 @ ( vd448 @ vmul ) @ ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) @ vplus ) )
= ( vd449 @ ( vd448 @ vmul ) @ ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(144,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
=> ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(194,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
=> ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(199,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(99,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(138,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ geq ) )
<=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(101,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ greater ) ) )
=> ( A @ ( B @ geq ) ) )
& ( ( A @ ( B @ geq ) )
=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ( A @ vsucc )
= ( B @ vsucc ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(249,plain,
! [A: $i,B: $i] :
( ( ( A @ vsucc )
= ( B @ vsucc ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ less ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(189,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ less ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ less ) )
& ( C @ ( B @ less ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
thf(93,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ less ) )
& ( C @ ( B @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ greater ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(152,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
=> ( A @ ( B @ greater ) ) )
& ( ( A @ ( B @ greater ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(216,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(50,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(238,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(132,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(74,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(260,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ greater ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(160,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ greater ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(70,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ geq ) )
& ( D @ ( C @ geq ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
thf(192,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ geq ) )
& ( D @ ( C @ geq ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(77,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ vsucc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(212,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(124,plain,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(47,axiom,
( ( vd449 @ ( vd448 @ vmul ) )
= ( v1 @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(293, 450, 1)') ).
thf(225,plain,
( ( vd449 @ ( vd448 @ vmul ) )
= ( v1 @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(148,plain,
! [A: $i,B: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(64,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ greater ) )
& ( D @ ( C @ geq ) ) )
| ( ( B @ ( A @ geq ) )
& ( D @ ( C @ greater ) ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
thf(113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ greater ) )
& ( D @ ( C @ geq ) ) )
| ( ( B @ ( A @ geq ) )
& ( D @ ( C @ greater ) ) ) )
=> ( D @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( vd449 @ ( A @ ( vd449 @ vmul ) @ vplus ) @ ( vd448 @ vmul ) )
= ( A @ vsucc @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 0)') ).
thf(219,plain,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( vd449 @ ( A @ ( vd449 @ vmul ) @ vplus ) @ ( vd448 @ vmul ) )
= ( A @ vsucc @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(140,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(66,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(135,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vmul ) )
= A )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(241,plain,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vmul ) )
= A )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(95,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(56,axiom,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( vd449 @ ( vd448 @ vmul ) @ ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) @ vplus ) )
= ( vd449 @ ( A @ ( vd449 @ vmul ) @ vplus ) @ ( vd448 @ vmul ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 1)') ).
thf(263,plain,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( vd449 @ ( vd448 @ vmul ) @ ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) @ vplus ) )
= ( vd449 @ ( A @ ( vd449 @ vmul ) @ vplus ) @ ( vd448 @ vmul ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
=> ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(186,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
=> ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(171,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( A @ vsucc @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ vsucc @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( A @ vsucc @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ vsucc @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(58,plain,
~ ! [A: $i] :
( ( ( A @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) )
=> ( ( A @ vsucc @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( A @ vsucc @ ( vd449 @ vmul ) @ ( vd448 @ vmul ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(235,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(207,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(42,axiom,
( ( v1 @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( vd449 @ ( vd448 @ vmul ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(293, 450, 0)') ).
thf(210,plain,
( ( v1 @ ( vd449 @ ( vd448 @ vmul ) @ vmul ) )
= ( vd449 @ ( vd448 @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(126,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ less ) )
& ( C @ ( B @ leq ) ) )
| ( ( B @ ( A @ leq ) )
& ( C @ ( B @ less ) ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ less ) )
& ( C @ ( B @ leq ) ) )
| ( ( B @ ( A @ leq ) )
& ( C @ ( B @ less ) ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(163,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
=> ( A @ ( B @ less ) ) )
& ( ( A @ ( B @ less ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( A @ ( B @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(68,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( A @ ( B @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(178,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ leq ) )
& ( C @ ( B @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
thf(111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ leq ) )
& ( C @ ( B @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
<=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
thf(83,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ less ) ) )
=> ( A @ ( B @ leq ) ) )
& ( ( A @ ( B @ leq ) )
=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(222,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(254,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(227,plain,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(429,plain,
$false,
inference(e,[status(thm)],[120,257,184,117,197,173,266,204,144,194,199,99,138,101,249,189,93,152,216,238,132,74,260,160,70,192,77,212,124,225,148,64,113,219,140,66,135,241,95,263,186,171,58,235,207,210,126,79,163,68,178,111,83,222,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n014.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 04:12:47 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.35/1.23 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.86/1.59 % [INFO] Parsing done (355ms).
% 2.27/1.61 % [INFO] Running in sequential loop mode.
% 3.09/2.17 % [INFO] eprover registered as external prover.
% 3.09/2.18 % [INFO] Scanning for conjecture ...
% 3.17/2.29 % [INFO] Found a conjecture (or negated_conjecture) and 55 axioms. Running axiom selection ...
% 3.35/2.37 % [INFO] Axiom selection finished. Selected 55 axioms (removed 0 axioms).
% 3.56/2.47 % [INFO] Problem is first-order (TPTP FOF).
% 3.56/2.48 % [INFO] Type checking passed.
% 3.56/2.49 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.90/3.82 % External prover 'e' found a proof!
% 7.90/3.82 % [INFO] Killing All external provers ...
% 7.90/3.82 % Time passed: 3235ms (effective reasoning time: 2206ms)
% 7.90/3.82 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.90/3.83 % Axioms used in derivation (55): ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 16), 1), ass(cond(228, 0), 0), ass(cond(20, 0), 0), ass(cond(241, 0), 0), ass(cond(12, 0), 0), ass(cond(140, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(223, 0), 0), ass(cond(conseq(292), 1), 2), ass(cond(conseq(292), 1), 3), ass(cond(goal(193), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(163, 0), 0), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 2), ass(cond(goal(88), 0), 1), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), holds(293, 450, 1), ass(cond(goal(193), 0), 1), ass(cond(189, 0), 0), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), ass(cond(goal(88), 0), 3), ass(cond(goal(202), 0), 2), ass(cond(270, 0), 0), ass(cond(184, 0), 0), ass(cond(goal(88), 0), 2), ass(cond(147, 0), 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(73, 0), 0), def(cond(conseq(axiom(3)), 17), 1), ass(cond(conseq(292), 1), 0), holds(293, 450, 0), ass(cond(goal(88), 0), 0), ass(cond(goal(202), 0), 1), ass(cond(goal(216), 0), 0), ass(cond(281, 0), 0), ass(cond(253, 0), 0), qu(antec(axiom(3)), imp(antec(axiom(3)))), ass(cond(209, 0), 0), ass(cond(261, 0), 0), ass(cond(52, 0), 0), ass(cond(158, 0), 0), ass(cond(234, 0), 0), ass(cond(33, 0), 0), qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)), ass(cond(61, 0), 0), ass(cond(goal(130), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(168, 0), 0), ass(cond(43, 0), 0), ass(cond(81, 0), 0), ass(cond(conseq(292), 1), 1)
% 7.90/3.83 % No. of inferences in proof: 114
% 7.90/3.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3235 ms resp. 2206 ms w/o parsing
% 8.26/3.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.26/3.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------