%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN612-1 : 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 : n009.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 09:17:58 AM UTC 2026
% Result : Unsatisfiable 16.62s 9.80s
% Output : Refutation 16.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 30
% Syntax : Number of formulae : 125 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 312 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1427 ( 161 ~; 127 |; 0 &;1139 @)
% ( 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 : 24 ( 21 usr; 6 con; 0-2 aty)
% Number of variables : 171 ( 0 ^; 171 !; 0 ?; 171 :)
% Comments :
%------------------------------------------------------------------------------
thf(p16_decl,type,
p16: $i > $o ).
thf(c21_decl,type,
c21: $i ).
thf(p2_decl,type,
p2: $i > $i > $o ).
thf(p5_decl,type,
p5: $i > $i > $o ).
thf(p3_decl,type,
p3: $i > $i > $o ).
thf(f7_decl,type,
f7: $i > $i ).
thf(c20_decl,type,
c20: $i ).
thf(f12_decl,type,
f12: $i > $i > $i ).
thf(c22_decl,type,
c22: $i ).
thf(f15_decl,type,
f15: $i > $i ).
thf(c19_decl,type,
c19: $i ).
thf(f4_decl,type,
f4: $i > $i ).
thf(f6_decl,type,
f6: $i > $i ).
thf(f8_decl,type,
f8: $i > $i ).
thf(f9_decl,type,
f9: $i > $i ).
thf(f13_decl,type,
f13: $i > $i ).
thf(p17_decl,type,
p17: $i > $i > $o ).
thf(p18_decl,type,
p18: $i > $i > $o ).
thf(f14_decl,type,
f14: $i > $i > $i ).
thf(f10_decl,type,
f10: $i > $i > $i ).
thf(f11_decl,type,
f11: $i > $i > $i ).
thf(6,negated_conjecture,
c22 @ f15 @ ( c21 @ ( c22 @ f12 ) @ p3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_6) ).
thf(35,plain,
c22 @ f15 @ ( c21 @ ( c22 @ f12 ) @ p3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,negated_conjecture,
~ ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p3_8) ).
thf(46,plain,
~ ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(68,plain,
~ ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(85,plain,
( ( ( c22 @ f15 @ ( c21 @ ( c22 @ f12 ) @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,68]) ).
thf(86,plain,
( ( c22 @ f15 @ ( c21 @ ( c22 @ f12 ) @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(88,plain,
( ( ( c20 @ f7 @ f6 @ f4 )
!= ( c22 @ f15 ) )
| ( ( c21 @ ( c22 @ f12 ) )
!= c19 ) ),
inference(simp,[status(thm)],[86]) ).
thf(27,negated_conjecture,
c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ f12 ) @ p3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_27) ).
thf(56,plain,
c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ f12 ) @ p3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(29,negated_conjecture,
c20 @ f8 @ f7 @ f6 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17_29) ).
thf(52,plain,
c20 @ f8 @ f7 @ f6 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22,negated_conjecture,
c20 @ f8 @ f7 @ f6 @ f4 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) @ p3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_22) ).
thf(55,plain,
c20 @ f8 @ f7 @ f6 @ f4 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) @ p3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,negated_conjecture,
! [A: $i] : ( A @ ( A @ p3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_4) ).
thf(47,plain,
! [A: $i] : ( A @ ( A @ p3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_19) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p3 ) )
!= ( C @ ( D @ p3 ) ) )
| ~ $true
| ~ ( B @ ( D @ p3 ) )
| ( C @ ( B @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[47,61]) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p3 ) )
!= ( C @ ( D @ p3 ) ) )
| ~ ( B @ ( D @ p3 ) )
| ( C @ ( B @ p3 ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p3 ) )
| ( A @ ( B @ p3 ) ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) @ p3 ) )
!= ( B @ ( A @ p3 ) ) )
| ~ $true
| ( A @ ( B @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[55,156]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) @ p3 ) )
!= ( B @ ( A @ p3 ) ) )
| ( A @ ( B @ p3 ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(238,plain,
c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) @ ( c20 @ f8 @ f7 @ f6 @ f4 @ p3 ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) )),bind(B,$thf( c20 @ f8 @ f7 @ f6 @ f4 ))]]) ).
thf(3,negated_conjecture,
! [A: $i] : ( A @ ( A @ p5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_3) ).
thf(42,plain,
! [A: $i] : ( A @ ( A @ p5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,negated_conjecture,
~ ( c20 @ f7 @ ( c21 @ p5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p5_5) ).
thf(31,plain,
~ ( c20 @ f7 @ ( c21 @ p5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(79,plain,
~ ( c20 @ f7 @ ( c21 @ p5 ) ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ ( A @ p5 ) )
!= ( c20 @ f7 @ ( c21 @ p5 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,79]) ).
thf(90,plain,
! [A: $i] :
( ( A @ ( A @ p5 ) )
!= ( c20 @ f7 @ ( c21 @ p5 ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
! [A: $i] :
( ( A
!= ( c20 @ f7 ) )
| ( A != c21 ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
( ( c20 @ f7 )
!= c21 ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
! [A: $i] :
( ( ( A @ ( A @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,68]) ).
thf(94,plain,
! [A: $i] :
( ( A @ ( A @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(95,plain,
! [A: $i] :
( ( A
!= ( c20 @ f7 @ f6 @ f4 ) )
| ( A != c19 ) ),
inference(simp,[status(thm)],[94]) ).
thf(96,plain,
( ( c20 @ f7 @ f6 @ f4 )
!= c19 ),
inference(simp,[status(thm)],[95]) ).
thf(7,negated_conjecture,
c22 @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_7) ).
thf(41,plain,
c22 @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(97,plain,
( ( ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55,68]) ).
thf(98,plain,
( ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
( ( ( c20 @ f8 @ f7 @ f6 @ f4 )
!= ( c20 @ f7 @ f6 @ f4 ) )
| ( ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) )
!= c19 ) ),
inference(simp,[status(thm)],[98]) ).
thf(103,plain,
( ( ( c20 @ f8 @ f7 @ f6 )
!= ( c20 @ f7 @ f6 ) )
| ( ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f12 ) )
!= c19 ) ),
inference(simp,[status(thm)],[99]) ).
thf(18,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_18) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( ( c22 @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
!= ( B @ ( A @ p3 ) ) )
| ~ $true
| ( A @ ( B @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[41,156]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( ( c22 @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
!= ( B @ ( A @ p3 ) ) )
| ( A @ ( B @ p3 ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
c21 @ ( c22 @ f15 @ f12 ) @ ( c22 @ p3 ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( c21 @ ( c22 @ f15 @ f12 ) )),bind(B,$thf( c22 ))]]) ).
thf(13,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f13 @ ( A @ f13 @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_13) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f13 @ ( A @ f13 @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(26,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p3 ) )
| ( D @ ( C @ f12 ) @ ( B @ ( A @ f12 ) @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_26) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p3 ) )
| ( D @ ( C @ f12 ) @ ( B @ ( A @ f12 ) @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c22 @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
!= ( B @ ( C @ p3 ) ) )
| ~ $true
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[41,61]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c22 @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
!= ( B @ ( C @ p3 ) ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
! [A: $i] :
( ~ ( A @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
| ( c22 @ ( A @ p3 ) ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( A )),bind(B,$thf( c22 )),bind(C,$thf( c21 @ ( c22 @ f15 @ f12 ) ))]]) ).
thf(189,plain,
! [A: $i] :
( ( ( A @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
!= ( c22 @ f15 @ ( c21 @ ( c22 @ f12 ) @ p3 ) ) )
| ~ $true
| ( c22 @ ( A @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[35,132]) ).
thf(190,plain,
! [A: $i] :
( ( ( A @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
!= ( c22 @ f15 @ ( c21 @ ( c22 @ f12 ) @ p3 ) ) )
| ( c22 @ ( A @ p3 ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(214,plain,
! [A: $i] :
( ( A
!= ( c22 @ f15 ) )
| ( ( c21 @ ( c22 @ f15 @ f12 ) )
!= ( c21 @ ( c22 @ f12 ) ) )
| ( c22 @ ( A @ p3 ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(220,plain,
( ( ( c21 @ ( c22 @ f15 @ f12 ) )
!= ( c21 @ ( c22 @ f12 ) ) )
| ( c22 @ ( c22 @ f15 @ p3 ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(2,negated_conjecture,
! [A: $i] : ( A @ ( A @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_2) ).
thf(38,plain,
! [A: $i] : ( A @ ( A @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(294,plain,
( ( ( c21 @ ( c22 @ f15 @ f12 ) @ ( c22 @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[232,68]) ).
thf(295,plain,
( ( c21 @ ( c22 @ f15 @ f12 ) @ ( c22 @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(297,plain,
( ( ( c21 @ ( c22 @ f15 @ f12 ) )
!= ( c20 @ f7 @ f6 @ f4 ) )
| ( c19 != c22 ) ),
inference(simp,[status(thm)],[295]) ).
thf(14,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p3 ) )
| ( B @ f15 @ ( A @ f15 @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_14) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p3 ) )
| ( B @ f15 @ ( A @ f15 @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(28,negated_conjecture,
! [A: $i] :
~ ( c20 @ f8 @ f7 @ f6 @ ( c21 @ ( A @ f12 ) @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p17_28) ).
thf(53,plain,
! [A: $i] :
~ ( c20 @ f8 @ f7 @ f6 @ ( c21 @ ( A @ f12 ) @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1,negated_conjecture,
~ ( c21 @ p16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21_is_not_p16_1) ).
thf(34,plain,
~ ( c21 @ p16 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(73,plain,
~ ( c21 @ p16 ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(30,negated_conjecture,
! [A: $i] :
( ~ ( c21 @ ( A @ p18 ) )
| ( c20 @ f8 @ f7 @ f6 @ ( A @ ( A @ f13 @ f12 ) @ ( c19 @ f11 ) @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f10 ) @ f9 @ p17 ) )
| ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) )
| ( c20 @ f7 @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_30) ).
thf(59,plain,
! [A: $i] :
( ~ ( c21 @ ( A @ p18 ) )
| ( c20 @ f8 @ f7 @ f6 @ ( A @ ( A @ f13 @ f12 ) @ ( c19 @ f11 ) @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f10 ) @ f9 @ p17 ) )
| ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) )
| ( c20 @ f7 @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(75,plain,
! [A: $i] :
( ~ ( c21 @ ( A @ p18 ) )
| ( c20 @ f8 @ f7 @ f6 @ ( A @ ( A @ f13 @ f12 ) @ ( c19 @ f11 ) @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f10 ) @ f9 @ p17 ) )
| ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) )
| ( c20 @ f7 @ ( A @ p5 ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(104,plain,
! [A: $i] :
( ~ ( c21 @ ( A @ p18 ) )
| ( c20 @ f8 @ f7 @ f6 @ ( A @ ( A @ f13 @ f12 ) @ ( c19 @ f11 ) @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f10 ) @ f9 @ p17 ) )
| $false
| ( c20 @ f7 @ ( A @ p5 ) ) ),
inference(rewrite,[status(thm)],[75,68]) ).
thf(105,plain,
! [A: $i] :
( ~ ( c21 @ ( A @ p18 ) )
| ( c20 @ f8 @ f7 @ f6 @ ( A @ ( A @ f13 @ f12 ) @ ( c19 @ f11 ) @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f10 ) @ f9 @ p17 ) )
| ( c20 @ f7 @ ( A @ p5 ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(11,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f6 @ ( A @ f6 @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f4 @ ( A @ f4 @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_15) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f4 @ ( A @ f4 @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f4 @ ( A @ f4 @ p3 ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(62,plain,
! [A: $i] :
~ ( c20 @ f8 @ f7 @ f6 @ ( c21 @ ( A @ f12 ) @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ) ),
inference(polarity_switch,[status(thm)],[53]) ).
thf(172,plain,
! [A: $i] :
( ( ( c20 @ f8 @ f7 @ f6 @ ( c21 @ ( A @ f12 ) @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ) )
!= ( c20 @ f8 @ f7 @ f6 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,62]) ).
thf(173,plain,
! [A: $i] :
( ( c20 @ f8 @ f7 @ f6 @ ( c21 @ ( A @ f12 ) @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ) )
!= ( c20 @ f8 @ f7 @ f6 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 @ p17 ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(176,plain,
! [A: $i] :
( ( ( c20 @ f8 @ f7 @ f6 )
!= ( c20 @ f8 @ f7 @ f6 ) )
| ( ( c21 @ ( A @ f12 ) @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 )
!= ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(178,plain,
! [A: $i] :
( ( c21 @ ( A @ f12 ) @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 )
!= ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) @ f9 ) ),
inference(simp,[status(thm)],[176]) ).
thf(180,plain,
! [A: $i] :
( ( c21 @ ( A @ f12 ) @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) )
!= ( c20 @ f8 @ f7 @ f6 @ f4 @ ( c19 @ ( c19 @ f9 @ f4 @ f14 ) @ f10 ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(10,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f8 @ ( A @ f8 @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_10) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f8 @ ( A @ f8 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f7 @ ( A @ f7 @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_16) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f7 @ ( A @ f7 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p18 ) )
| ~ ( B @ ( D @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18_21) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p18 ) )
| ~ ( B @ ( D @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p18 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( ( c22 @ f15 @ ( c21 @ ( c22 @ f12 ) @ p3 ) )
!= ( B @ ( A @ p3 ) ) )
| ~ $true
| ( A @ ( B @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[35,156]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( ( c22 @ f15 @ ( c21 @ ( c22 @ f12 ) @ p3 ) )
!= ( B @ ( A @ p3 ) ) )
| ( A @ ( B @ p3 ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(235,plain,
c21 @ ( c22 @ f12 ) @ ( c22 @ f15 @ p3 ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( c21 @ ( c22 @ f12 ) )),bind(B,$thf( c22 @ f15 ))]]) ).
thf(311,plain,
( ( ( c21 @ ( c22 @ f12 ) @ ( c22 @ f15 @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,68]) ).
thf(312,plain,
( ( c21 @ ( c22 @ f12 ) @ ( c22 @ f15 @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) ),
inference(simp,[status(thm)],[311]) ).
thf(313,plain,
( ( ( c21 @ ( c22 @ f12 ) )
!= ( c20 @ f7 @ f6 @ f4 ) )
| ( ( c22 @ f15 )
!= c19 ) ),
inference(simp,[status(thm)],[312]) ).
thf(24,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p3 ) )
| ~ ( C @ ( A @ p3 ) )
| ( D @ ( C @ f10 ) @ ( B @ ( A @ f10 ) @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_24) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p3 ) )
| ~ ( C @ ( A @ p3 ) )
| ( D @ ( C @ f10 ) @ ( B @ ( A @ f10 ) @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p5 ) )
| ~ ( B @ p16 )
| ( A @ p16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_9) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p5 ) )
| ~ ( B @ p16 )
| ( A @ p16 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p5 ) )
| ~ ( B @ p16 )
| ( A @ p16 ) ),
inference(cnf,[status(esa)],[36]) ).
thf(17,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_17) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ f12 ) @ p3 ) )
!= ( B @ ( A @ p3 ) ) )
| ~ $true
| ( A @ ( B @ p3 ) ) ),
inference(paramod_ordered,[status(thm)],[56,156]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ ( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ f12 ) @ p3 ) )
!= ( B @ ( A @ p3 ) ) )
| ( A @ ( B @ p3 ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ f12 ) @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ p3 ),
inference(pattern_uni,[status(thm)],[225:[bind(A,$thf( c21 @ ( c20 @ f8 @ f7 @ f6 @ f4 @ f15 @ f12 ) )),bind(B,$thf( c20 @ f8 @ f7 @ f6 @ f4 @ f15 ))]]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(25,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p3 ) )
| ~ ( C @ ( A @ p3 ) )
| ( D @ ( C @ f11 ) @ ( B @ ( A @ f11 ) @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_25) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p3 ) )
| ~ ( C @ ( A @ p3 ) )
| ( D @ ( C @ f11 ) @ ( B @ ( A @ f11 ) @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(181,plain,
! [A: $i] :
( ( ( c21 @ ( A @ f12 ) )
!= ( c20 @ f8 @ f7 @ f6 @ f4 ) )
| ( ( c19 @ ( c19 @ f9 @ f4 @ f14 ) )
!= ( c19 @ ( c19 @ f9 @ f4 @ f14 ) ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(182,plain,
! [A: $i] :
( ( c21 @ ( A @ f12 ) )
!= ( c20 @ f8 @ f7 @ f6 @ f4 ) ),
inference(simp,[status(thm)],[181]) ).
thf(83,plain,
( ( ( c22 @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,68]) ).
thf(84,plain,
( ( c22 @ ( c21 @ ( c22 @ f15 @ f12 ) @ p3 ) )
!= ( c20 @ f7 @ f6 @ f4 @ ( c19 @ p3 ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(87,plain,
( ( ( c20 @ f7 @ f6 @ f4 )
!= c22 )
| ( ( c21 @ ( c22 @ f15 @ f12 ) )
!= c19 ) ),
inference(simp,[status(thm)],[84]) ).
thf(12,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p3 ) )
| ( B @ f9 @ ( A @ f9 @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p3 ) )
| ( B @ f9 @ ( A @ f9 @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p3 ) )
| ~ ( C @ ( A @ p3 ) )
| ( D @ ( C @ f14 ) @ ( B @ ( A @ f14 ) @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_23) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p3 ) )
| ~ ( C @ ( A @ p3 ) )
| ( D @ ( C @ f14 ) @ ( B @ ( A @ f14 ) @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(20,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p17 ) )
| ~ ( B @ ( D @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17_20) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p17 ) )
| ~ ( B @ ( D @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p17 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2039,plain,
$false,
inference(e,[status(thm)],[88,56,52,238,92,96,41,103,43,79,232,42,37,46,57,61,132,60,220,38,297,33,156,53,73,105,45,64,180,32,34,44,59,54,313,49,81,39,226,35,48,63,50,182,31,99,87,40,55,58,235,36,51,47,68,62,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN612-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/5.41 % Computer : n009.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Sat Sep 26 18:16:20 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.41 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/6.21 % [INFO] Parsing done (204ms).
% 1.41/6.22 % [INFO] Running in sequential loop mode.
% 2.14/6.64 % [INFO] eprover registered as external prover.
% 2.14/6.65 % [INFO] Scanning for conjecture ...
% 2.53/6.80 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.53/6.89 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.53/6.89 % [INFO] Problem is propositional (TPTP CNF).
% 2.53/6.89 % [INFO] Type checking passed.
% 2.73/6.90 % [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 ...
% 16.04/9.79 % External prover 'e' found a proof!
% 16.04/9.80 % [INFO] Killing All external provers ...
% 16.62/9.80 % Time passed: 4242ms (effective reasoning time: 3570ms)
% 16.62/9.80 % Axioms used in derivation (0):
% 16.62/9.80 % No. of inferences in proof: 125
% 16.62/9.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4242 ms resp. 3570 ms w/o parsing
% 16.62/9.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.62/9.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------