%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 08:10:12 AM UTC 2026
% Result : Theorem 26.70s 5.43s
% Output : Refutation 23.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 63
% Syntax : Number of formulae : 213 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 431 ( 224 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1364 ( 153 ~; 92 |; 34 &;1013 @)
% ( 4 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 367 ( 0 ^; 347 !; 20 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(vmul_decl,type,
vmul: $i > $i > $i ).
thf(vd508_decl,type,
vd508: $i ).
thf(vd511_decl,type,
vd511: $i ).
thf(vd509_decl,type,
vd509: $i ).
thf(vd512_decl,type,
vd512: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(v1_decl,type,
v1: $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(vskolem2_decl,type,
vskolem2: $i > $i ).
thf(35,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(193,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ vsucc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(170,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(171,plain,
~ ? [A: $i] :
( ( A @ vsucc )
= A ),
inference(miniscope,[status(thm)],[170]) ).
thf(172,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(cnf,[status(esa)],[171]) ).
thf(173,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(lifteq,[status(thm)],[172]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(80,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(154,plain,
! [A: $i,B: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( A @ ( B @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(101,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( A @ ( B @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(249,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(217,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(52,axiom,
vd509 @ ( vd512 @ vmul ) @ ( vd509 @ ( vd511 @ vmul ) @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 1)') ).
thf(247,plain,
vd509 @ ( vd512 @ vmul ) @ ( vd509 @ ( vd511 @ vmul ) @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ vmul ) )
= ( B @ ( C @ vmul ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(307)), 0), 0)') ).
thf(202,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ vmul ) )
= ( B @ ( C @ vmul ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ less ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(174,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)],[29]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(185,plain,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(53,axiom,
vd509 @ ( vd508 @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(314), 510, 0)') ).
thf(248,plain,
vd509 @ ( vd508 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1,conjecture,
vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(315), 516, 0)') ).
thf(2,negated_conjecture,
~ ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(65,plain,
~ ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(284,plain,
( ( ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) )
!= ( vd509 @ ( vd508 @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[248,65]) ).
thf(285,plain,
( ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) )
!= ( vd509 @ ( vd508 @ greater ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(288,plain,
( ( ( vd512 @ ( vd509 @ vmul ) )
!= vd509 )
| ( ( vd511 @ ( vd508 @ vmul ) )
!= vd508 ) ),
inference(simp,[status(thm)],[285]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(254,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[254]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(257,plain,
! [A: $i] :
~ ( A @ ( A @ greater ) ),
inference(simp,[status(thm)],[256]) ).
thf(58,axiom,
vd511 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
thf(259,plain,
vd511 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(55,axiom,
( ( vd511 @ ( vd509 @ vmul ) )
= ( vd509 @ ( vd511 @ vmul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 0)') ).
thf(252,plain,
( ( vd511 @ ( vd509 @ vmul ) )
= ( vd509 @ ( vd511 @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(253,plain,
( ( vd511 @ ( vd509 @ vmul ) )
= ( vd509 @ ( vd511 @ vmul ) ) ),
inference(lifteq,[status(thm)],[252]) ).
thf(367,plain,
vd509 @ ( vd511 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ),
inference(rewrite,[status(thm)],[259,253]) ).
thf(368,plain,
( ( ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) )
!= ( vd509 @ ( vd511 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,65]) ).
thf(369,plain,
( ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) )
!= ( vd509 @ ( vd511 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(378,plain,
( ( ( vd512 @ ( vd509 @ vmul ) )
!= ( vd509 @ ( vd511 @ vmul ) ) )
| ( ( vd511 @ ( vd508 @ vmul ) )
!= ( vd511 @ ( vd508 @ vmul ) ) ) ),
inference(simp,[status(thm)],[369]) ).
thf(382,plain,
( ( vd512 @ ( vd509 @ vmul ) )
!= ( vd509 @ ( vd511 @ vmul ) ) ),
inference(simp,[status(thm)],[378]) ).
thf(389,plain,
( ( vd512 != vd509 )
| ( vd509 != vd511 ) ),
inference(simp,[status(thm)],[382]) ).
thf(32,axiom,
! [A: $i] : ( v1 @ ( A @ geq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
thf(183,plain,
! [A: $i] : ( v1 @ ( A @ geq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(184,plain,
! [A: $i] : ( v1 @ ( A @ geq ) ),
inference(cnf,[status(esa)],[183]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( A @ ( B @ vmul ) )
= ( A @ ( C @ vmul ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 1)') ).
thf(189,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( A @ ( B @ vmul ) )
= ( A @ ( C @ vmul ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(57,axiom,
vd512 @ ( vd511 @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(314), 513, 0)') ).
thf(258,plain,
vd512 @ ( vd511 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(286,plain,
( ( ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) )
!= ( vd512 @ ( vd511 @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[258,65]) ).
thf(287,plain,
( ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) )
!= ( vd512 @ ( vd511 @ greater ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(289,plain,
( ( ( vd512 @ ( vd509 @ vmul ) )
!= vd512 )
| ( ( vd511 @ ( vd508 @ vmul ) )
!= vd511 ) ),
inference(simp,[status(thm)],[287]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vmul ) )
= A )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(207,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)],[40]) ).
thf(208,plain,
( ! [A: $i] :
( ( v1 @ ( A @ vmul ) )
= A )
& ! [A: $i,B: $i] :
( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
inference(miniscope,[status(thm)],[207]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( C @ vmul ) )
= C )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
inference(cnf,[status(esa)],[208]) ).
thf(211,plain,
! [A: $i] :
( ( v1 @ ( A @ vmul ) )
= A ),
inference(cnfConj,[status(thm)],[209]) ).
thf(213,plain,
! [A: $i] :
( ( v1 @ ( A @ vmul ) )
= A ),
inference(lifteq,[status(thm)],[211]) ).
thf(214,plain,
! [A: $i] :
( ( v1 @ ( A @ vmul ) )
= A ),
inference(simp,[status(thm)],[213]) ).
thf(400,plain,
! [A: $i] :
( ( ( v1 @ ( A @ vmul ) )
!= ( vd511 @ ( vd508 @ vmul ) ) )
| ( ( vd512 @ ( vd509 @ vmul ) )
!= vd509 )
| ( A != vd508 ) ),
inference(paramod_ordered,[status(thm)],[214,288]) ).
thf(436,plain,
( ( v1 != vd511 )
| ( vd508 != vd508 )
| ( ( vd512 @ ( vd509 @ vmul ) )
!= vd509 ) ),
inference(simp,[status(thm)],[400]) ).
thf(448,plain,
( ( v1 != vd511 )
| ( ( vd512 @ ( vd509 @ vmul ) )
!= vd509 ) ),
inference(simp,[status(thm)],[436]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(106,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(38,axiom,
( ( vd509 @ ( vd512 @ vmul ) )
= ( vd512 @ ( vd509 @ vmul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 2)') ).
thf(200,plain,
( ( vd509 @ ( vd512 @ vmul ) )
= ( vd512 @ ( vd509 @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(201,plain,
( ( vd509 @ ( vd512 @ vmul ) )
= ( vd512 @ ( vd509 @ vmul ) ) ),
inference(lifteq,[status(thm)],[200]) ).
thf(337,plain,
vd512 @ ( vd509 @ vmul ) @ ( vd509 @ ( vd511 @ vmul ) @ greater ),
inference(rewrite,[status(thm)],[247,201]) ).
thf(340,plain,
( ( ( vd512 @ ( vd509 @ vmul ) @ ( vd509 @ ( vd511 @ vmul ) @ greater ) )
!= ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,65]) ).
thf(341,plain,
( ( vd512 @ ( vd509 @ vmul ) @ ( vd509 @ ( vd511 @ vmul ) @ greater ) )
!= ( vd512 @ ( vd509 @ vmul ) @ ( vd511 @ ( vd508 @ vmul ) @ greater ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(348,plain,
( ( ( vd512 @ ( vd509 @ vmul ) )
!= ( vd512 @ ( vd509 @ vmul ) ) )
| ( ( vd509 @ ( vd511 @ vmul ) )
!= ( vd511 @ ( vd508 @ vmul ) ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(353,plain,
( ( vd509 @ ( vd511 @ vmul ) )
!= ( vd511 @ ( vd508 @ vmul ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(390,plain,
( ( ( vd512 @ ( vd509 @ vmul ) )
!= ( vd511 @ ( vd509 @ vmul ) ) )
| ( ( vd509 @ ( vd511 @ vmul ) )
!= ( vd509 @ ( vd511 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[253,382]) ).
thf(391,plain,
( ( vd512 @ ( vd509 @ vmul ) )
!= ( vd511 @ ( vd509 @ vmul ) ) ),
inference(simp,[status(thm)],[390]) ).
thf(393,plain,
( ( vd512 != vd511 )
| ( vd509 != vd509 ) ),
inference(simp,[status(thm)],[391]) ).
thf(397,plain,
vd512 != vd511,
inference(simp,[status(thm)],[393]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
thf(280,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)],[64]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(89,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(233,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
<=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
thf(108,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)],[15]) ).
thf(109,plain,
( ! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ less ) ) )
=> ( A @ ( B @ leq ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ) ),
inference(miniscope,[status(thm)],[108]) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ leq ) )
| ( D != C ) )
& ( ( C @ ( D @ leq ) )
| ~ ( C @ ( D @ less ) ) )
& ( ( B = A )
| ( A @ ( B @ less ) )
| ~ ( A @ ( B @ leq ) ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B != A ) ),
inference(cnfConj,[status(thm)],[110]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[113]) ).
thf(117,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[116]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(220,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)],[43]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ greater ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(260,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)],[59]) ).
thf(413,plain,
! [A: $i] :
( ( ( v1 @ ( A @ vmul ) )
!= ( vd512 @ ( vd509 @ vmul ) ) )
| ( A
!= ( vd509 @ ( vd511 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[214,382]) ).
thf(429,plain,
( ( v1 != vd512 )
| ( ( vd509 @ ( vd511 @ vmul ) )
!= vd509 ) ),
inference(simp,[status(thm)],[413]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(229,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
=> ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(224,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)],[45]) ).
thf(186,plain,
~ ? [A: $i] :
( ( A @ vsucc )
= v1 ),
inference(miniscope,[status(thm)],[185]) ).
thf(187,plain,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
inference(cnf,[status(esa)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( A @ vsucc )
!= v1 ),
inference(lifteq,[status(thm)],[187]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(141,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ less ) )
& ( C @ ( B @ less ) ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
thf(134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ less ) )
& ( C @ ( B @ less ) ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(68,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)],[4]) ).
thf(69,plain,
( ! [A: $i] :
( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ! [A: $i,B: $i] :
( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
inference(miniscope,[status(thm)],[68]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v1 @ ( C @ vplus ) )
= ( C @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(271,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(272,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(cnf,[status(esa)],[271]) ).
thf(273,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(lifteq,[status(thm)],[272]) ).
thf(410,plain,
! [A: $i] :
( ( ( v1 @ ( A @ vmul ) )
!= ( vd509 @ ( vd511 @ vmul ) ) )
| ( A
!= ( vd511 @ ( vd508 @ vmul ) ) ) ),
inference(paramod_ordered,[status(thm)],[214,353]) ).
thf(433,plain,
( ( v1 != vd509 )
| ( ( vd511 @ ( vd508 @ vmul ) )
!= vd511 ) ),
inference(simp,[status(thm)],[410]) ).
thf(516,plain,
! [A: $i] :
( ( ( A @ ( v1 @ vmul ) )
!= ( vd511 @ ( vd508 @ vmul ) ) )
| ( v1 != vd509 )
| ( A != vd511 ) ),
inference(paramod_ordered,[status(thm)],[273,433]) ).
thf(538,plain,
( ( vd511 != vd511 )
| ( v1 != vd508 )
| ( v1 != vd509 ) ),
inference(simp,[status(thm)],[516]) ).
thf(558,plain,
( ( v1 != vd508 )
| ( v1 != vd509 ) ),
inference(simp,[status(thm)],[538]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(128,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ geq ) )
<=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(237,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)],[51]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
thf(166,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)],[27]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
thf(148,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)],[23]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(180,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(401,plain,
! [A: $i] :
( ( ( v1 @ ( A @ vmul ) )
!= ( vd512 @ ( vd509 @ vmul ) ) )
| ( A != vd509 )
| ( ( vd511 @ ( vd508 @ vmul ) )
!= vd508 ) ),
inference(paramod_ordered,[status(thm)],[214,288]) ).
thf(425,plain,
( ( v1 != vd512 )
| ( vd509 != vd509 )
| ( ( vd511 @ ( vd508 @ vmul ) )
!= vd508 ) ),
inference(simp,[status(thm)],[401]) ).
thf(444,plain,
( ( v1 != vd512 )
| ( ( vd511 @ ( vd508 @ vmul ) )
!= vd508 ) ),
inference(simp,[status(thm)],[425]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( A @ vsucc )
= ( B @ vsucc ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(118,plain,
! [A: $i,B: $i] :
( ( ( A @ vsucc )
= ( B @ vsucc ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(144,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(simp,[status(thm)],[143]) ).
thf(493,plain,
! [A: $i] :
( ( ( v1 @ ( A @ vmul ) )
!= ( vd511 @ ( vd508 @ vmul ) ) )
| ( v1 != vd512 )
| ( A != vd508 ) ),
inference(paramod_ordered,[status(thm)],[214,444]) ).
thf(497,plain,
( ( v1 != vd511 )
| ( vd508 != vd508 )
| ( v1 != vd512 ) ),
inference(simp,[status(thm)],[493]) ).
thf(498,plain,
( ( v1 != vd511 )
| ( v1 != vd512 ) ),
inference(simp,[status(thm)],[497]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(274,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)],[62]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(76,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(98,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)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(103,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ leq ) )
& ( C @ ( B @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
thf(66,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ leq ) )
& ( C @ ( B @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ greater ) )
=> ( A @ ( C @ vmul ) @ ( A @ ( B @ vmul ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
thf(198,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ greater ) )
=> ( A @ ( C @ vmul ) @ ( A @ ( B @ vmul ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(477,plain,
! [A: $i] :
( ( ( vd509 @ ( vd508 @ greater ) )
!= ( A @ ( A @ greater ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[248,257]) ).
thf(478,plain,
! [A: $i] :
( ( vd509 @ ( vd508 @ greater ) )
!= ( A @ ( A @ greater ) ) ),
inference(simp,[status(thm)],[477]) ).
thf(483,plain,
! [A: $i] :
( ( vd509 != A )
| ( vd508 != A ) ),
inference(simp,[status(thm)],[478]) ).
thf(487,plain,
vd509 != vd508,
inference(simp,[status(thm)],[483]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(123,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(145,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(150,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(95,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)],[10]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
=> ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(177,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)],[30]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ less ) )
=> ( A @ ( C @ vmul ) @ ( A @ ( B @ vmul ) @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 0)') ).
thf(231,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ less ) )
=> ( A @ ( C @ vmul ) @ ( A @ ( B @ vmul ) @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(87,plain,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(158,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)],[26]) ).
thf(72,plain,
! [A: $i] :
( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(74,plain,
! [A: $i] :
( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(75,plain,
! [A: $i] :
( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) ),
inference(simp,[status(thm)],[74]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(235,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(238,plain,
( ! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ greater ) ) )
=> ( A @ ( B @ geq ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ geq ) )
=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ) ),
inference(miniscope,[status(thm)],[237]) ).
thf(239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ geq ) )
| ( D != C ) )
& ( ( C @ ( D @ geq ) )
| ~ ( C @ ( D @ greater ) ) )
& ( ( B = A )
| ( A @ ( B @ greater ) )
| ~ ( A @ ( B @ geq ) ) ) ),
inference(cnf,[status(esa)],[238]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ( B != A ) ),
inference(cnfConj,[status(thm)],[239]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ geq ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(246,plain,
! [A: $i] : ( A @ ( A @ geq ) ),
inference(simp,[status(thm)],[245]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(136,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ greater ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(268,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)],[60]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ vplus ) )
!= A ),
inference(simp,[status(thm)],[78]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(195,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(277,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(215,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ vmul ) @ ( B @ ( A @ vmul ) @ less ) )
=> ( C @ ( A @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ vmul ) @ ( B @ ( A @ vmul ) @ less ) )
=> ( C @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ vmul ) @ ( B @ ( A @ vmul ) @ greater ) )
=> ( C @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(307), 0), 0)') ).
thf(227,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ vmul ) @ ( B @ ( A @ vmul ) @ greater ) )
=> ( C @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(354,plain,
( ( vd509 != vd511 )
| ( vd511 != vd508 ) ),
inference(simp,[status(thm)],[353]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(83,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)],[7]) ).
thf(8181,plain,
$false,
inference(e,[status(thm)],[193,173,80,154,101,249,170,217,247,202,174,185,288,257,389,184,189,289,448,253,106,353,397,280,89,233,248,117,201,220,260,429,229,252,65,224,188,141,134,73,558,128,237,166,148,180,444,118,259,382,144,498,274,76,98,271,367,103,66,198,108,487,123,145,150,95,67,177,231,87,258,158,75,433,207,214,235,246,183,273,136,268,79,195,200,68,277,337,215,222,254,227,354,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.39 % Computer : n001.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Sat Sep 26 04:19:12 UTC 2026
% 0.15/0.39 % CPUTime :
% 0.15/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.62/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.00/0.82 % [INFO] Parsing done (127ms).
% 1.00/0.83 % [INFO] Running in sequential loop mode.
% 1.36/1.03 % [INFO] eprover registered as external prover.
% 1.71/1.03 % [INFO] Scanning for conjecture ...
% 1.71/1.08 % [INFO] Found a conjecture (or negated_conjecture) and 62 axioms. Running axiom selection ...
% 1.71/1.12 % [INFO] Axiom selection finished. Selected 62 axioms (removed 0 axioms).
% 1.96/1.19 % [INFO] Problem is first-order (TPTP FOF).
% 1.96/1.19 % [INFO] Type checking passed.
% 1.96/1.20 % [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 ...
% 26.70/5.42 % External prover 'e' found a proof!
% 26.70/5.42 % [INFO] Killing All external provers ...
% 26.70/5.42 % Time passed: 4935ms (effective reasoning time: 4589ms)
% 26.70/5.42 % 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)>
% 26.70/5.43 % Axioms used in derivation (62): ass(cond(223, 0), 0), ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 16), 1), holds(conjunct1(315), 514, 0), ass(cond(241, 0), 0), ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(81, 0), 0), ass(cond(conjunct2(conjunct2(307)), 0), 0), 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(299, 0), 0), ass(cond(299, 0), 2), ass(cond(299, 0), 1), ass(cond(goal(88), 0), 1), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), ass(cond(goal(193), 0), 1), ass(cond(189, 0), 0), holds(conjunct1(314), 510, 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(228, 0), 0), holds(conjunct2(315), 515, 2), 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), ass(cond(goal(88), 0), 0), def(cond(conseq(axiom(3)), 17), 1), holds(conjunct2(314), 513, 0), ass(cond(conjunct1(307), 0), 0), ass(cond(20, 0), 0), ass(cond(goal(202), 0), 1), ass(cond(goal(216), 0), 0), ass(cond(281, 0), 0), holds(conjunct2(315), 515, 1), 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(conjunct1(conjunct2(307)), 0), 0), ass(cond(158, 0), 0), ass(cond(234, 0), 0), ass(cond(33, 0), 0), ass(cond(290, 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), def(cond(conseq(axiom(3)), 12), 1), holds(conjunct2(315), 515, 0)
% 26.70/5.43 % No. of inferences in proof: 213
% 26.70/5.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4935 ms resp. 4589 ms w/o parsing
% 23.55/5.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.55/5.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------