%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN571-1 : 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 : n026.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 09:17:52 AM UTC 2026
% Result : Unsatisfiable 9.49s 3.82s
% Output : Refutation 8.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 132 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 351 ( 81 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1325 ( 186 ~; 135 |; 0 &;1004 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 301 ( 0 ^; 301 !; 0 ?; 301 :)
% Comments :
%------------------------------------------------------------------------------
thf(p4_decl,type,
p4: $i > $i > $o ).
thf(p2_decl,type,
p2: $i > $i > $o ).
thf(p11_decl,type,
p11: $i > $i > $o ).
thf(f5_decl,type,
f5: $i > $i ).
thf(c14_decl,type,
c14: $i ).
thf(c13_decl,type,
c13: $i ).
thf(f3_decl,type,
f3: $i > $i > $i ).
thf(f6_decl,type,
f6: $i > $i ).
thf(f7_decl,type,
f7: $i > $i ).
thf(c12_decl,type,
c12: $i ).
thf(f10_decl,type,
f10: $i > $i ).
thf(f9_decl,type,
f9: $i > $i > $i ).
thf(f8_decl,type,
f8: $i > $i > $i ).
thf(5,negated_conjecture,
! [B: $i,A: $i] :
( ( A @ ( B @ p11 ) )
| ( B @ ( A @ p11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_5) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ p11 ) )
| ( B @ ( A @ p11 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ p11 ) )
| ( B @ ( A @ p11 ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ p11 ) )
!= ( B @ ( A @ p11 ) ) )
| ( B @ ( A @ p11 ) ) ),
inference(eqfactor_ordered,[status(thm)],[46]) ).
thf(73,plain,
! [A: $i] : ( A @ ( A @ p11 ) ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( B ))]]) ).
thf(74,plain,
! [A: $i] : ( A @ ( A @ p11 ) ),
inference(simp,[status(thm)],[73]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ~ ( A @ ( A @ f10 @ f5 @ p11 ) )
| ( A @ ( c14 @ p11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_7) ).
thf(32,plain,
! [A: $i] :
( ~ ( A @ ( A @ f10 @ f5 @ p11 ) )
| ( A @ ( c14 @ p11 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(49,plain,
! [A: $i] :
( ~ ( A @ ( A @ f10 @ f5 @ p11 ) )
| ( A @ ( c14 @ p11 ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ p11 ) )
!= ( B @ ( B @ f10 @ f5 @ p11 ) ) )
| ~ $true
| ( B @ ( c14 @ p11 ) ) ),
inference(paramod_ordered,[status(thm)],[74,49]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ p11 ) )
!= ( B @ ( B @ f10 @ f5 @ p11 ) ) )
| ( B @ ( c14 @ p11 ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ f10 @ f5 ) )
| ( B @ ( c14 @ p11 ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(96,plain,
! [A: $i] :
( ( ( A @ f10 @ f5 )
!= A )
| ( A @ ( c14 @ p11 ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(6,negated_conjecture,
! [A: $i] :
~ ( c12 @ f7 @ f6 @ f5 @ ( A @ f3 ) @ ( A @ p11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p11_6) ).
thf(26,plain,
! [A: $i] :
~ ( c12 @ f7 @ f6 @ f5 @ ( A @ f3 ) @ ( A @ p11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(54,plain,
! [A: $i] :
~ ( c12 @ f7 @ f6 @ f5 @ ( A @ f3 ) @ ( A @ p11 ) ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(521,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c14 @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( B @ f3 ) @ ( B @ p11 ) ) )
| ~ $true
| ( ( A @ f10 @ f5 )
!= A ) ),
inference(paramod_ordered,[status(thm)],[96,54]) ).
thf(522,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c14 @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( B @ f3 ) @ ( B @ p11 ) ) )
| ( ( A @ f10 @ f5 )
!= A ) ),
inference(simp,[status(thm)],[521]) ).
thf(523,plain,
( ( c12 @ f7 @ f6 @ f5 @ ( c14 @ f3 ) @ f10 @ f5 )
!= ( c12 @ f7 @ f6 @ f5 @ ( c14 @ f3 ) ) ),
inference(pattern_uni,[status(thm)],[522:[bind(A,$thf( c12 @ f7 @ f6 @ f5 @ ( c14 @ f3 ) )),bind(B,$thf( c14 ))]]) ).
thf(17,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p11 ) )
| ~ ( B @ ( D @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_17) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p11 ) )
| ~ ( B @ ( D @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p11 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p11 ) )
| ~ ( B @ ( D @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p11 ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(16,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ f3 ) @ ( A @ p11 ) )
| ( C @ ( B @ ( A @ f9 ) @ p11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_16) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ f3 ) @ ( A @ p11 ) )
| ( C @ ( B @ ( A @ f9 ) @ p11 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ f3 ) @ ( A @ p11 ) )
| ( C @ ( B @ ( A @ f9 ) @ p11 ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p11 ) )
!= ( C @ ( D @ f3 ) @ ( B @ p11 ) ) )
| ~ $true
| ( D @ ( C @ ( B @ f9 ) @ p11 ) ) ),
inference(paramod_ordered,[status(thm)],[74,42]) ).
thf(250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p11 ) )
!= ( C @ ( D @ f3 ) @ ( B @ p11 ) ) )
| ( D @ ( C @ ( B @ f9 ) @ p11 ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(251,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ p11 ) ),
inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( F @ ( E @ f3 ) )),bind(B,$thf( F @ ( E @ f3 ) )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(295,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ p11 ) ),
inference(simp,[status(thm)],[251]) ).
thf(4,negated_conjecture,
! [A: $i] :
~ ( A @ f5 @ ( c13 @ p11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p11_4) ).
thf(39,plain,
! [A: $i] :
~ ( A @ f5 @ ( c13 @ p11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(41,plain,
! [A: $i] :
~ ( A @ f5 @ ( c13 @ p11 ) ),
inference(polarity_switch,[status(thm)],[39]) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ p11 ) )
!= ( C @ f5 @ ( c13 @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[295,41]) ).
thf(301,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ p11 ) )
!= ( C @ f5 @ ( c13 @ p11 ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ f5 ) )
| ( ( B @ ( B @ ( A @ f3 ) @ f9 ) )
!= c13 ) ),
inference(simp,[status(thm)],[301]) ).
thf(317,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ f5 @ f3 ) @ f9 ) )
!= c13 ),
inference(simp,[status(thm)],[312]) ).
thf(3,negated_conjecture,
! [A: $i] : ( c14 @ ( A @ f5 @ p11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_3) ).
thf(33,plain,
! [A: $i] : ( c14 @ ( A @ f5 @ p11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ f9 ) @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( D @ f3 ) @ ( D @ p11 ) ) )
| ~ $true
| ~ ( B @ ( C @ f3 ) @ ( A @ p11 ) ) ),
inference(paramod_ordered,[status(thm)],[42,54]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ f9 ) @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( D @ f3 ) @ ( D @ p11 ) ) )
| ~ ( B @ ( C @ f3 ) @ ( A @ p11 ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(276,plain,
! [B: $i,A: $i] :
~ ( B @ ( c12 @ f7 @ f6 @ f5 @ ( B @ ( A @ f9 ) @ f3 ) @ f3 ) @ ( A @ p11 ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( c12 @ f7 @ f6 @ f5 @ ( J @ ( I @ f9 ) @ f3 ) )),bind(D,$thf( J @ ( I @ f9 ) ))]]) ).
thf(288,plain,
! [B: $i,A: $i] :
~ ( B @ ( c12 @ f7 @ f6 @ f5 @ ( B @ ( A @ f9 ) @ f3 ) @ f3 ) @ ( A @ p11 ) ),
inference(simp,[status(thm)],[276]) ).
thf(403,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c14 @ ( A @ f5 @ p11 ) )
!= ( C @ ( c12 @ f7 @ f6 @ f5 @ ( C @ ( B @ f9 ) @ f3 ) @ f3 ) @ ( B @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,288]) ).
thf(404,plain,
! [C: $i,B: $i,A: $i] :
( ( c14 @ ( A @ f5 @ p11 ) )
!= ( C @ ( c12 @ f7 @ f6 @ f5 @ ( C @ ( B @ f9 ) @ f3 ) @ f3 ) @ ( B @ p11 ) ) ),
inference(simp,[status(thm)],[403]) ).
thf(420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c12 @ f7 @ f6 @ f5 @ ( C @ ( B @ f9 ) @ f3 ) @ f3 ) )
!= c14 )
| ( ( A @ f5 )
!= B ) ),
inference(simp,[status(thm)],[404]) ).
thf(426,plain,
! [B: $i,A: $i] :
( ( B @ ( c12 @ f7 @ f6 @ f5 @ ( B @ ( A @ f5 @ f9 ) @ f3 ) @ f3 ) )
!= c14 ),
inference(simp,[status(thm)],[420]) ).
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(75,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ p11 ) )
!= ( B @ f5 @ ( c13 @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,41]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ p11 ) )
!= ( B @ f5 @ ( c13 @ p11 ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ f5 ) )
| ( A != c13 ) ),
inference(simp,[status(thm)],[76]) ).
thf(82,plain,
! [A: $i] :
( ( A @ f5 )
!= c13 ),
inference(simp,[status(thm)],[79]) ).
thf(401,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p11 ) )
!= ( C @ ( c12 @ f7 @ f6 @ f5 @ ( C @ ( B @ f9 ) @ f3 ) @ f3 ) @ ( B @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,288]) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ p11 ) )
!= ( C @ ( c12 @ f7 @ f6 @ f5 @ ( C @ ( B @ f9 ) @ f3 ) @ f3 ) @ ( B @ p11 ) ) ),
inference(simp,[status(thm)],[401]) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( c12 @ f7 @ f6 @ f5 @ ( C @ ( B @ f9 ) @ f3 ) @ f3 ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[402]) ).
thf(427,plain,
! [B: $i,A: $i] :
( ( B @ ( c12 @ f7 @ f6 @ f5 @ ( B @ ( A @ f9 ) @ f3 ) @ f3 ) )
!= A ),
inference(simp,[status(thm)],[421]) ).
thf(20,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p2 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f9 ) @ ( B @ ( A @ f9 ) @ 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 @ f9 ) @ ( B @ ( A @ f9 ) @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f7 @ ( A @ f7 @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_8) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f7 @ ( A @ f7 @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
! [A: $i] : ( A @ ( A @ p4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_1) ).
thf(25,plain,
! [A: $i] : ( A @ ( A @ p4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p11 ) )
!= ( C @ ( C @ f10 @ f5 @ p11 ) ) )
| ~ $true
| ( C @ ( c14 @ p11 ) )
| ( B @ ( A @ p11 ) ) ),
inference(paramod_ordered,[status(thm)],[46,49]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p11 ) )
!= ( C @ ( C @ f10 @ f5 @ p11 ) ) )
| ( C @ ( c14 @ p11 ) )
| ( B @ ( A @ p11 ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
! [A: $i] :
( ( A @ ( c14 @ p11 ) )
| ( A @ f10 @ f5 @ ( A @ p11 ) ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( A )),bind(B,$thf( A @ f10 @ f5 )),bind(C,$thf( A ))]]) ).
thf(305,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ p11 ) )
!= ( D @ ( E @ f3 ) @ ( C @ p11 ) ) )
| ~ $true
| ( E @ ( D @ ( C @ f9 ) @ p11 ) ) ),
inference(paramod_ordered,[status(thm)],[295,42]) ).
thf(306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ p11 ) )
!= ( D @ ( E @ f3 ) @ ( C @ p11 ) ) )
| ( E @ ( D @ ( C @ f9 ) @ p11 ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( A @ ( C @ ( B @ f3 ) @ f3 ) @ f9 ) @ f9 ) @ p11 ) ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$thf( K @ ( J @ f3 ) )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( K @ ( J @ f3 ) @ f3 ) @ f9 ) )),bind(D,$thf( K )),bind(E,$thf( J ))]]) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( A @ ( C @ ( B @ f3 ) @ f3 ) @ f9 ) @ f9 ) @ p11 ) ),
inference(simp,[status(thm)],[307]) ).
thf(2,negated_conjecture,
! [A: $i] : ( A @ ( A @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_2) ).
thf(29,plain,
! [A: $i] : ( A @ ( A @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(210,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( c14 @ p11 ) )
!= ( A @ f10 @ f5 @ ( A @ p11 ) ) )
| ( A @ f10 @ f5 @ ( A @ p11 ) ) ),
inference(eqfactor_ordered,[status(thm)],[93]) ).
thf(215,plain,
! [A: $i] :
( ( ( A @ f10 @ f5 )
!= A )
| ( c14 != A )
| ( A @ f10 @ f5 @ ( A @ p11 ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(221,plain,
( ( ( c14 @ f10 @ f5 )
!= c14 )
| ( c14 @ f10 @ f5 @ ( c14 @ p11 ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( ( A @ f10 @ f5 @ ( A @ p11 ) )
!= ( B @ f5 @ ( c13 @ p11 ) ) )
| ~ $true
| ( A @ ( c14 @ p11 ) ) ),
inference(paramod_ordered,[status(thm)],[93,41]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( ( A @ f10 @ f5 @ ( A @ p11 ) )
!= ( B @ f5 @ ( c13 @ p11 ) ) )
| ( A @ ( c14 @ p11 ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(193,plain,
c13 @ ( c14 @ p11 ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( c13 )),bind(B,$thf( c13 @ f10 ))]]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( ( c13 @ ( c14 @ p11 ) )
!= ( B @ ( c12 @ f7 @ f6 @ f5 @ ( B @ ( A @ f9 ) @ f3 ) @ f3 ) @ ( A @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[193,288]) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( c13 @ ( c14 @ p11 ) )
!= ( B @ ( c12 @ f7 @ f6 @ f5 @ ( B @ ( A @ f9 ) @ f3 ) @ f3 ) @ ( A @ p11 ) ) ),
inference(simp,[status(thm)],[405]) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c12 @ f7 @ f6 @ f5 @ ( B @ ( A @ f9 ) @ f3 ) @ f3 ) )
!= c13 )
| ( c14 != A ) ),
inference(simp,[status(thm)],[406]) ).
thf(428,plain,
! [A: $i] :
( ( A @ ( c12 @ f7 @ f6 @ f5 @ ( A @ ( c14 @ f9 ) @ f3 ) @ f3 ) )
!= c13 ),
inference(simp,[status(thm)],[422]) ).
thf(13,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_13) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p4 ) )
| ~ ( A @ ( C @ p4 ) )
| ( B @ ( A @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,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_19) ).
thf(38,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)],[19]) ).
thf(18,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p4 ) )
| ~ ( C @ ( A @ p4 ) )
| ( D @ ( C @ f8 ) @ ( B @ ( A @ f8 ) @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_18) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p4 ) )
| ~ ( C @ ( A @ p4 ) )
| ( D @ ( C @ f8 ) @ ( B @ ( A @ f8 ) @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f10 @ ( A @ f10 @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_10) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f10 @ ( A @ f10 @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p2 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f9 ) @ ( B @ ( A @ f9 ) @ p2 ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ p11 ) )
!= ( D @ ( E @ f3 ) @ ( C @ p11 ) ) )
| ~ $true
| ( E @ ( D @ ( C @ f9 ) @ p11 ) )
| ( A @ ( B @ p11 ) ) ),
inference(paramod_ordered,[status(thm)],[46,42]) ).
thf(265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ p11 ) )
!= ( D @ ( E @ f3 ) @ ( C @ p11 ) ) )
| ( E @ ( D @ ( C @ f9 ) @ p11 ) )
| ( A @ ( B @ p11 ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ f9 ) @ p11 ) )
| ( A @ ( C @ ( B @ f3 ) @ p11 ) ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( A )),bind(B,$thf( G @ ( F @ f3 ) )),bind(C,$thf( A )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ f9 ) @ p11 ) )
| ( A @ ( C @ ( B @ f3 ) @ p11 ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(9,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f5 @ ( A @ f5 @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_9) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f5 @ ( A @ f5 @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( B @ f3 ) @ ( B @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,54]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( B @ f3 ) @ ( B @ p11 ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( A
!= ( c12 @ f7 @ f6 @ f5 @ ( B @ f3 ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[78]) ).
thf(81,plain,
! [A: $i] :
( ( c12 @ f7 @ f6 @ f5 @ ( A @ f3 ) )
!= A ),
inference(simp,[status(thm)],[80]) ).
thf(107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ p11 ) )
!= ( E @ f5 @ ( c13 @ p11 ) ) )
| ~ $true
| ~ ( D @ ( C @ p11 ) )
| ~ ( B @ ( D @ p2 ) )
| ~ ( A @ ( C @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[56,41]) ).
thf(108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ p11 ) )
!= ( E @ f5 @ ( c13 @ p11 ) ) )
| ~ ( D @ ( C @ p11 ) )
| ~ ( B @ ( D @ p2 ) )
| ~ ( A @ ( C @ p2 ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ p11 ) )
| ~ ( C @ f5 @ ( B @ p2 ) )
| ~ ( c13 @ ( A @ p2 ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( c13 )),bind(B,$thf( F @ f5 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ p11 ) )
| ~ ( C @ f5 @ ( B @ p2 ) )
| ~ ( c13 @ ( A @ p2 ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ ( c14 @ p11 ) )
!= ( B @ ( A @ p11 ) ) )
| ~ $true
| ~ ( C @ f5 @ ( B @ p2 ) )
| ~ ( c13 @ ( A @ p2 ) ) ),
inference(paramod_ordered,[status(thm)],[193,140]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c13 @ ( c14 @ p11 ) )
!= ( B @ ( A @ p11 ) ) )
| ~ ( C @ f5 @ ( B @ p2 ) )
| ~ ( c13 @ ( A @ p2 ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
! [A: $i] :
( ~ ( A @ f5 @ ( c13 @ p2 ) )
| ~ ( c13 @ ( c14 @ p2 ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( c14 )),bind(B,$thf( c13 ))]]) ).
thf(240,plain,
! [A: $i] :
( ~ ( A @ f5 @ ( c13 @ p2 ) )
| ~ ( c13 @ ( c14 @ p2 ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(233,plain,
! [A: $i] :
( ( ( c13 @ ( c14 @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( A @ f3 ) @ ( A @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[193,54]) ).
thf(234,plain,
! [A: $i] :
( ( c13 @ ( c14 @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( A @ f3 ) @ ( A @ p11 ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(237,plain,
! [A: $i] :
( ( ( c12 @ f7 @ f6 @ f5 @ ( A @ f3 ) )
!= c13 )
| ( c14 != A ) ),
inference(simp,[status(thm)],[234]) ).
thf(241,plain,
( ( c12 @ f7 @ f6 @ f5 @ ( c14 @ f3 ) )
!= c13 ),
inference(simp,[status(thm)],[237]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( ( c14 @ ( A @ f5 @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( B @ f3 ) @ ( B @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,54]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( c14 @ ( A @ f5 @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( B @ f3 ) @ ( B @ p11 ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( c12 @ f7 @ f6 @ f5 @ ( B @ f3 ) )
!= c14 )
| ( ( A @ f5 )
!= B ) ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
! [A: $i] :
( ( c12 @ f7 @ f6 @ f5 @ ( A @ f5 @ f3 ) )
!= c14 ),
inference(simp,[status(thm)],[62]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ p2 ) )
!= ( c13 @ ( c14 @ p2 ) ) )
| ~ ( B @ f5 @ ( c13 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,240]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ p2 ) )
!= ( c13 @ ( c14 @ p2 ) ) )
| ~ ( B @ f5 @ ( c13 @ p2 ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( A != c13 )
| ( A != c14 )
| ~ ( B @ f5 @ ( c13 @ p2 ) ) ),
inference(simp,[status(thm)],[322]) ).
thf(336,plain,
! [A: $i] :
( ( c13 != c14 )
| ~ ( A @ f5 @ ( c13 @ p2 ) ) ),
inference(simp,[status(thm)],[332]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( C @ f3 ) @ ( C @ p11 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[295,54]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ p11 ) )
!= ( c12 @ f7 @ f6 @ f5 @ ( C @ f3 ) @ ( C @ p11 ) ) ),
inference(simp,[status(thm)],[308]) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c12 @ f7 @ f6 @ f5 @ ( C @ f3 ) ) )
| ( ( B @ ( B @ ( A @ f3 ) @ f9 ) )
!= C ) ),
inference(simp,[status(thm)],[309]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( c12 @ f7 @ f6 @ f5 @ ( B @ ( B @ ( A @ f3 ) @ f9 ) @ f3 ) )
!= A ),
inference(simp,[status(thm)],[314]) ).
thf(15,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ f9 ) @ p11 ) )
| ( C @ ( B @ f3 ) @ ( A @ p11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_15) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ f9 ) @ p11 ) )
| ( C @ ( B @ f3 ) @ ( A @ p11 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,negated_conjecture,
! [B: $i,A: $i] : ( B @ ( A @ f8 ) @ f5 @ ( B @ f5 @ ( A @ f5 @ f9 ) @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_14) ).
thf(23,plain,
! [B: $i,A: $i] : ( B @ ( A @ f8 ) @ f5 @ ( B @ f5 @ ( A @ f5 @ f9 ) @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f6 @ ( A @ f6 @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_11) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f6 @ ( A @ f6 @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(726,plain,
$false,
inference(e,[status(thm)],[523,56,317,41,426,31,82,427,42,24,288,37,25,46,93,316,29,221,428,74,21,33,28,38,193,96,32,34,22,44,286,27,54,49,81,39,140,240,241,35,63,295,336,43,319,40,26,23,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN571-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n026.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 18:17:10 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.09/1.14 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.69/1.44 % [INFO] Parsing done (285ms).
% 1.69/1.46 % [INFO] Running in sequential loop mode.
% 2.52/2.00 % [INFO] eprover registered as external prover.
% 2.52/2.01 % [INFO] Scanning for conjecture ...
% 2.79/2.13 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.08/2.20 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.08/2.20 % [INFO] Problem is propositional (TPTP CNF).
% 3.08/2.20 % [INFO] Type checking passed.
% 3.08/2.21 % [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 ...
% 9.49/3.81 % External prover 'e' found a proof!
% 9.49/3.81 % [INFO] Killing All external provers ...
% 9.49/3.81 % Time passed: 3210ms (effective reasoning time: 2346ms)
% 9.49/3.82 % Axioms used in derivation (0):
% 9.49/3.82 % No. of inferences in proof: 132
% 9.49/3.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3210 ms resp. 2346 ms w/o parsing
% 8.92/3.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.92/3.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------