%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN572-1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n005.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 09:17:53 AM UTC 2026
% Result : Unsatisfiable 43.32s 10.28s
% Output : Refutation 37.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 122 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 318 ( 49 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1581 ( 155 ~; 122 |; 0 &;1304 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 240 ( 0 ^; 240 !; 0 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
thf(p2_decl,type,
p2: $i > $i > $o ).
thf(p6_decl,type,
p6: $i > $i > $o ).
thf(p4_decl,type,
p4: $i > $i > $o ).
thf(f10_decl,type,
f10: $i > $i ).
thf(f9_decl,type,
f9: $i > $i ).
thf(f3_decl,type,
f3: $i > $i > $i ).
thf(f5_decl,type,
f5: $i > $i ).
thf(f7_decl,type,
f7: $i > $i ).
thf(f8_decl,type,
f8: $i > $i ).
thf(c13_decl,type,
c13: $i ).
thf(p12_decl,type,
p12: $i > $i > $o ).
thf(f11_decl,type,
f11: $i > $i > $i ).
thf(c14_decl,type,
c14: $i ).
thf(c15_decl,type,
c15: $i ).
thf(5,negated_conjecture,
! [A: $i] : ( A @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_5) ).
thf(21,plain,
! [A: $i] : ( A @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f9 @ ( A @ f9 @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_8) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f9 @ ( A @ f9 @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f9 @ ( A @ f9 @ p2 ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[21,44]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
! [A: $i] : ( A @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( D )),bind(B,$thf( c13 @ f8 @ f7 @ f5 @ ( D @ f3 ) )),bind(C,$thf( D ))]]) ).
thf(129,plain,
! [A: $i] : ( A @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ p2 ) ),
inference(simp,[status(thm)],[121]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[129,44]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
! [A: $i] : ( A @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( J )),bind(B,$thf( c13 @ f8 @ f7 @ f5 @ ( J @ f3 ) @ f9 )),bind(C,$thf( J @ f9 ))]]) ).
thf(136,plain,
! [A: $i] : ( A @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ p2 ) ),
inference(simp,[status(thm)],[135]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[136,44]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
! [A: $i] : ( A @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( L )),bind(B,$thf( c13 @ f8 @ f7 @ f5 @ ( L @ f3 ) @ f9 @ f9 )),bind(C,$thf( L @ f9 @ f9 ))]]) ).
thf(261,plain,
! [A: $i] : ( A @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ p2 ) ),
inference(simp,[status(thm)],[259]) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[261,44]) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(314,plain,
! [A: $i] : ( A @ f9 @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( N )),bind(B,$thf( c13 @ f8 @ f7 @ f5 @ ( N @ f3 ) @ f9 @ f9 @ f9 )),bind(C,$thf( N @ f9 @ f9 @ f9 ))]]) ).
thf(317,plain,
! [A: $i] : ( A @ f9 @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ p2 ) ),
inference(simp,[status(thm)],[314]) ).
thf(18,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p12 ) )
| ~ ( B @ ( D @ p4 ) )
| ~ ( A @ ( C @ p4 ) )
| ( B @ ( A @ p12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_18) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p12 ) )
| ~ ( B @ ( D @ p4 ) )
| ~ ( A @ ( C @ p4 ) )
| ( B @ ( A @ p12 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p12 ) )
| ~ ( B @ ( D @ p4 ) )
| ~ ( A @ ( C @ p4 ) )
| ( B @ ( A @ p12 ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(12,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
! [A: $i] : ( A @ ( A @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
thf(25,plain,
! [A: $i] : ( A @ ( A @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p2 ) )
!= ( C @ ( D @ p2 ) ) )
| ~ $true
| ~ ( B @ ( D @ p2 ) )
| ( C @ ( B @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[25,42]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p2 ) )
!= ( C @ ( D @ p2 ) ) )
| ~ ( B @ ( D @ p2 ) )
| ( C @ ( B @ p2 ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( A @ ( B @ p2 ) ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f9 @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[317,44]) ).
thf(454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f9 @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[453]) ).
thf(455,plain,
! [A: $i] : ( A @ f9 @ f9 @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[454:[bind(A,$thf( P )),bind(B,$thf( c13 @ f8 @ f7 @ f5 @ ( P @ f3 ) @ f9 @ f9 @ f9 @ f9 )),bind(C,$thf( P @ f9 @ f9 @ f9 @ f9 ))]]) ).
thf(464,plain,
! [A: $i] : ( A @ f9 @ f9 @ f9 @ f9 @ f9 @ ( c13 @ f8 @ f7 @ f5 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ f9 @ p2 ) ),
inference(simp,[status(thm)],[455]) ).
thf(20,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p2 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f3 ) @ ( B @ ( A @ f3 ) @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_20) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p2 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f3 ) @ ( B @ ( A @ f3 ) @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2,negated_conjecture,
! [A: $i] : ( A @ ( A @ p6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_2) ).
thf(29,plain,
! [A: $i] : ( A @ ( A @ p6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,negated_conjecture,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ ( A @ f9 @ ( A @ f3 ) @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
thf(36,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ ( A @ f9 @ ( A @ f3 ) @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ ( A @ f9 @ ( A @ f3 ) @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[36,44]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ ( A @ f9 @ ( A @ f3 ) @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(124,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( F )),bind(B,$thf( F @ f9 @ ( F @ f3 ) )),bind(C,$thf( c13 @ f8 @ f7 @ f5 ))]]) ).
thf(130,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ p2 ) ),
inference(simp,[status(thm)],[124]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[130,44]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( G )),bind(B,$thf( G @ f9 @ ( G @ f3 ) @ f9 )),bind(C,$thf( c13 @ f8 @ f7 @ f5 @ f9 ))]]) ).
thf(168,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ p2 ) ),
inference(simp,[status(thm)],[167]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[168,44]) ).
thf(270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(271,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( H )),bind(B,$thf( H @ f9 @ ( H @ f3 ) @ f9 @ f9 )),bind(C,$thf( c13 @ f8 @ f7 @ f5 @ f9 @ f9 ))]]) ).
thf(274,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ p2 ) ),
inference(simp,[status(thm)],[271]) ).
thf(433,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[274,44]) ).
thf(434,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[433]) ).
thf(435,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[434:[bind(A,$thf( I )),bind(B,$thf( I @ f9 @ ( I @ f3 ) @ f9 @ f9 @ f9 )),bind(C,$thf( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 ))]]) ).
thf(443,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ p2 ) ),
inference(simp,[status(thm)],[435]) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ~ $true
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[443,44]) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ p2 ) )
!= ( C @ ( B @ p2 ) ) )
| ( C @ f9 @ ( B @ f9 @ p2 ) ) ),
inference(simp,[status(thm)],[473]) ).
thf(475,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ f9 @ p2 ) ),
inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( J )),bind(B,$thf( J @ f9 @ ( J @ f3 ) @ f9 @ f9 @ f9 @ f9 )),bind(C,$thf( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ f9 ))]]) ).
thf(485,plain,
! [A: $i] : ( c13 @ f8 @ f7 @ f5 @ f9 @ f9 @ f9 @ f9 @ f9 @ ( A @ f9 @ ( A @ f3 ) @ f9 @ f9 @ f9 @ f9 @ f9 @ p2 ) ),
inference(simp,[status(thm)],[475]) ).
thf(3,negated_conjecture,
! [A: $i] : ( A @ ( A @ p4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_3) ).
thf(33,plain,
! [A: $i] : ( A @ ( A @ p4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,negated_conjecture,
~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( c14 @ f10 @ p12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p12_16) ).
thf(35,plain,
~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( c14 @ f10 @ p12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,plain,
~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( c14 @ f10 @ p12 ) ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ p12 ) )
!= ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( c14 @ f10 @ p12 ) ) )
| ~ $true
| ~ ( D @ ( C @ p12 ) )
| ~ ( B @ ( D @ p4 ) )
| ~ ( A @ ( C @ p4 ) ) ),
inference(paramod_ordered,[status(thm)],[48,41]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ p12 ) )
!= ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( c14 @ f10 @ p12 ) ) )
| ~ ( D @ ( C @ p12 ) )
| ~ ( B @ ( D @ p4 ) )
| ~ ( A @ ( C @ p4 ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p12 ) )
| ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( B @ p4 ) )
| ~ ( c14 @ f10 @ ( A @ p4 ) ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( c14 @ f10 )),bind(B,$thf( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p12 ) )
| ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( B @ p4 ) )
| ~ ( c14 @ f10 @ ( A @ p4 ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p4 ) )
!= ( c14 @ f10 @ ( B @ p4 ) ) )
| ~ ( C @ ( B @ p12 ) )
| ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( C @ p4 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,70]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p4 ) )
!= ( c14 @ f10 @ ( B @ p4 ) ) )
| ~ ( C @ ( B @ p12 ) )
| ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( C @ p4 ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
! [A: $i] :
( ~ ( A @ ( c14 @ f10 @ p12 ) )
| ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( A @ p4 ) ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( c14 @ f10 )),bind(B,$thf( c14 @ f10 )),bind(C,$thf( C ))]]) ).
thf(84,plain,
! [A: $i] :
( ~ ( A @ ( c14 @ f10 @ p12 ) )
| ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( A @ p4 ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ ( C @ p2 ) )
!= ( A @ ( C @ p2 ) ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p2 ) )
| ( A @ ( A @ p2 ) ) ),
inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( B ))]]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p2 ) )
| ( A @ ( A @ p2 ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p4 ) )
!= ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( C @ p4 ) ) )
| ~ ( C @ ( B @ p12 ) )
| ~ $true
| ~ ( c14 @ f10 @ ( B @ p4 ) ) ),
inference(paramod_ordered,[status(thm)],[33,70]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p4 ) )
!= ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( C @ p4 ) ) )
| ~ ( C @ ( B @ p12 ) )
| ~ ( c14 @ f10 @ ( B @ p4 ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
! [A: $i] :
( ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( A @ p12 ) )
| ~ ( c14 @ f10 @ ( A @ p4 ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) )),bind(B,$thf( B )),bind(C,$thf( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) ))]]) ).
thf(85,plain,
! [A: $i] :
( ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( A @ p12 ) )
| ~ ( c14 @ f10 @ ( A @ p4 ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(15,negated_conjecture,
! [B: $i,A: $i] : ( B @ f10 @ ( A @ f10 @ f11 ) @ ( B @ ( A @ f3 ) @ f10 @ p12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_15) ).
thf(40,plain,
! [B: $i,A: $i] : ( B @ f10 @ ( A @ f10 @ f11 ) @ ( B @ ( A @ f3 ) @ f10 @ p12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ f10 @ ( A @ f10 @ f11 ) @ ( B @ ( A @ f3 ) @ f10 @ p12 ) )
!= ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( C @ p12 ) ) )
| ~ $true
| ~ ( c14 @ f10 @ ( C @ p4 ) ) ),
inference(paramod_ordered,[status(thm)],[40,85]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ f10 @ ( A @ f10 @ f11 ) @ ( B @ ( A @ f3 ) @ f10 @ p12 ) )
!= ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( C @ p12 ) ) )
| ~ ( c14 @ f10 @ ( C @ p4 ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
~ ( c14 @ f10 @ ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 @ p4 ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( c15 @ ( c14 @ f3 ) )),bind(B,$thf( c15 )),bind(C,$thf( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 ))]]) ).
thf(13,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p6 ) )
| ~ ( A @ ( C @ p6 ) )
| ( B @ ( A @ p6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_13) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p6 ) )
| ~ ( A @ ( C @ p6 ) )
| ( B @ ( A @ p6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p4 ) )
| ~ ( C @ ( A @ p4 ) )
| ( D @ ( C @ f11 ) @ ( B @ ( A @ f11 ) @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_19) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p4 ) )
| ~ ( C @ ( A @ p4 ) )
| ( D @ ( C @ f11 ) @ ( B @ ( A @ f11 ) @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,negated_conjecture,
! [A: $i] : ( A @ f10 @ ( A @ f9 @ f10 @ p4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_4) ).
thf(39,plain,
! [A: $i] : ( A @ f10 @ ( A @ f9 @ f10 @ p4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(169,plain,
! [A: $i] :
( ( ( A @ f10 @ ( A @ f9 @ f10 @ p4 ) )
!= ( c14 @ f10 @ ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 @ p4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,160]) ).
thf(170,plain,
! [A: $i] :
( ( A @ f10 @ ( A @ f9 @ f10 @ p4 ) )
!= ( c14 @ f10 @ ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 @ p4 ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ f10 )
!= ( c14 @ f10 ) )
| ( ( A @ f9 @ f10 )
!= ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(276,plain,
! [A: $i] :
( ( A != c14 )
| ( ( A @ f9 @ f10 )
!= ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(297,plain,
( ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 )
!= ( c14 @ f9 @ f10 ) ),
inference(simp,[status(thm)],[276]) ).
thf(277,plain,
! [A: $i] :
( ( A != c14 )
| ( ( A @ f9 )
!= ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(298,plain,
( ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) )
!= ( c14 @ f9 ) ),
inference(simp,[status(thm)],[277]) ).
thf(7,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f5 @ ( A @ f5 @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_7) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f5 @ ( A @ f5 @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ ( A @ p4 ) )
!= ( c14 @ f10 @ ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 @ p4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,160]) ).
thf(172,plain,
! [A: $i] :
( ( A @ ( A @ p4 ) )
!= ( c14 @ f10 @ ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 @ p4 ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(174,plain,
! [A: $i] :
( ( A
!= ( c14 @ f10 ) )
| ( A
!= ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(175,plain,
( ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) @ f10 )
!= ( c14 @ f10 ) ),
inference(simp,[status(thm)],[174]) ).
thf(176,plain,
( ( c15 @ ( c15 @ ( c14 @ f3 ) @ f3 ) )
!= c14 ),
inference(simp,[status(thm)],[175]) ).
thf(10,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p6 ) )
| ( B @ f7 @ ( A @ f7 @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_10) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p6 ) )
| ( B @ f7 @ ( A @ f7 @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f10 @ ( A @ f10 @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_9) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f10 @ ( A @ f10 @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( ( A @ f10 @ ( A @ f9 @ f10 @ p4 ) )
!= ( c14 @ f10 @ ( B @ p4 ) ) )
| ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( B @ p12 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,85]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( ( A @ f10 @ ( A @ f9 @ f10 @ p4 ) )
!= ( c14 @ f10 @ ( B @ p4 ) ) )
| ~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( B @ p12 ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
~ ( c15 @ f10 @ ( c15 @ ( c14 @ f3 ) @ f10 @ f11 ) @ ( c14 @ f9 @ f10 @ p12 ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( c14 )),bind(B,$thf( c14 @ f9 @ f10 ))]]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p2 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f3 ) @ ( B @ ( A @ f3 ) @ p2 ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(6,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p6 ) )
| ( B @ f8 @ ( A @ f8 @ p6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_6) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p6 ) )
| ( B @ f8 @ ( A @ f8 @ p6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p4 ) )
| ~ ( A @ ( C @ p4 ) )
| ( B @ ( A @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_14) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p4 ) )
| ~ ( A @ ( C @ p4 ) )
| ( B @ ( A @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,negated_conjecture,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ f3 ) @ f3 ) @ ( C @ ( B @ f3 ) @ ( A @ f3 ) @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_17) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ f3 ) @ f3 ) @ ( C @ ( B @ f3 ) @ ( A @ f3 ) @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5487,plain,
$false,
inference(e,[status(thm)],[317,48,31,203,136,464,42,24,37,25,261,29,443,485,84,233,85,160,21,33,28,38,297,70,173,129,41,298,32,34,176,22,44,27,274,39,130,35,154,175,43,40,26,23,36,168,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN572-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.12 % 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
% 0.23/0.49 % Computer : n005.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 18:14:16 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.45/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.62 % [INFO] Parsing done (282ms).
% 1.99/1.65 % [INFO] Running in sequential loop mode.
% 2.99/2.26 % [INFO] eprover registered as external prover.
% 2.99/2.27 % [INFO] Scanning for conjecture ...
% 3.38/2.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.56/2.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.56/2.56 % [INFO] Problem is propositional (TPTP CNF).
% 3.56/2.57 % [INFO] Type checking passed.
% 3.56/2.57 % [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 ...
% 43.32/10.27 % External prover 'e' found a proof!
% 43.32/10.27 % [INFO] Killing All external provers ...
% 43.32/10.27 % Time passed: 9576ms (effective reasoning time: 8620ms)
% 43.32/10.28 % Axioms used in derivation (0):
% 43.32/10.28 % No. of inferences in proof: 122
% 43.32/10.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9576 ms resp. 8620 ms w/o parsing
% 37.35/10.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 37.35/10.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------