%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN631-1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n011.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 09:18:01 AM UTC 2026
% Result : Unsatisfiable 52.21s 11.05s
% Output : Refutation 43.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of formulae : 131 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 339 ( 63 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1462 ( 196 ~; 166 |; 0 &;1100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 8 con; 0-3 aty)
% Number of variables : 286 ( 0 ^; 286 !; 0 ?; 286 :)
% Comments :
%------------------------------------------------------------------------------
thf(p10_decl,type,
p10: $i > $i > $o ).
thf(p9_decl,type,
p9: $i > $i > $o ).
thf(p7_decl,type,
p7: $i > $i > $o ).
thf(p6_decl,type,
p6: $i > $i > $o ).
thf(p5_decl,type,
p5: $i > $i > $o ).
thf(p3_decl,type,
p3: $i > $i > $o ).
thf(p2_decl,type,
p2: $i > $i > $o ).
thf(p12_decl,type,
p12: $i > $i > $o ).
thf(p22_decl,type,
p22: $i > $i > $o ).
thf(c25_decl,type,
c25: $i ).
thf(c28_decl,type,
c28: $i ).
thf(f17_decl,type,
f17: $i > $i ).
thf(f18_decl,type,
f18: $i > $i > $i ).
thf(f16_decl,type,
f16: $i > $i ).
thf(p23_decl,type,
p23: $i > $i > $o ).
thf(f13_decl,type,
f13: $i > $i > $i ).
thf(c27_decl,type,
c27: $i ).
thf(f14_decl,type,
f14: $i > $i ).
thf(f11_decl,type,
f11: $i > $i ).
thf(f15_decl,type,
f15: $i > $i ).
thf(c24_decl,type,
c24: $i ).
thf(f4_decl,type,
f4: $i > $i ).
thf(f20_decl,type,
f20: $i > $i ).
thf(p21_decl,type,
p21: $i > $i > $o ).
thf(c29_decl,type,
c29: $i ).
thf(f19_decl,type,
f19: $i > $i > $i > $i ).
thf(f8_decl,type,
f8: $i > $i > $i > $i ).
thf(c26_decl,type,
c26: $i ).
thf(12,negated_conjecture,
c24 @ f15 @ f11 @ ( c28 @ f14 @ ( c27 @ f13 ) @ p23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_12) ).
thf(47,plain,
c24 @ f15 @ f11 @ ( c28 @ f14 @ ( c27 @ f13 ) @ p23 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,negated_conjecture,
~ ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p23_13) ).
thf(45,plain,
~ ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(89,plain,
~ ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) ),
inference(polarity_switch,[status(thm)],[45]) ).
thf(113,plain,
( ( ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) )
!= ( c24 @ f15 @ f11 @ ( c28 @ f14 @ ( c27 @ f13 ) @ p23 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,89]) ).
thf(114,plain,
( ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) )
!= ( c24 @ f15 @ f11 @ ( c28 @ f14 @ ( c27 @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(115,plain,
( ( ( c24 @ f15 @ f11 )
!= ( c24 @ f11 ) )
| ( ( c28 @ f14 @ ( c27 @ f16 @ f13 ) )
!= ( c28 @ f14 @ ( c27 @ f13 ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(25,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_25) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,negated_conjecture,
! [A: $i] : ( A @ ( A @ p10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_1) ).
thf(42,plain,
! [A: $i] : ( A @ ( A @ p10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
! [A: $i] : ( A @ ( A @ p6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_4) ).
thf(52,plain,
! [A: $i] : ( A @ ( A @ p6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(121,plain,
( ( ( c24 @ f15 )
!= c24 )
| ( ( c28 @ f14 @ ( c27 @ f16 @ f13 ) )
!= ( c28 @ f14 @ ( c27 @ f13 ) ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(15,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p9 ) )
| ( B @ f11 @ ( A @ f11 @ p10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_15) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p9 ) )
| ( B @ f11 @ ( A @ f11 @ p10 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p9 ) )
| ( B @ f15 @ ( A @ f15 @ p9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_14) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p9 ) )
| ( B @ f15 @ ( A @ f15 @ p9 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p7 ) )
| ~ ( A @ ( C @ p7 ) )
| ( B @ ( A @ p7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_23) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p7 ) )
| ~ ( A @ ( C @ p7 ) )
| ( B @ ( A @ p7 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(22,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p9 ) )
| ~ ( A @ ( C @ p9 ) )
| ( B @ ( A @ p9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_22) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p9 ) )
| ~ ( A @ ( C @ p9 ) )
| ( B @ ( A @ p9 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f4 @ ( A @ f4 @ p3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_16) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f4 @ ( A @ f4 @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f4 @ ( A @ f4 @ p3 ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(120,plain,
( ( ( c24 @ f15 @ f11 )
!= ( c24 @ f11 ) )
| ( ( c28 @ f14 )
!= ( c28 @ f14 ) )
| ( ( c27 @ f16 )
!= c27 ) ),
inference(simp,[status(thm)],[115]) ).
thf(123,plain,
( ( ( c24 @ f15 @ f11 )
!= ( c24 @ f11 ) )
| ( ( c27 @ f16 )
!= c27 ) ),
inference(simp,[status(thm)],[120]) ).
thf(5,negated_conjecture,
! [A: $i] : ( A @ ( A @ p5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_5) ).
thf(39,plain,
! [A: $i] : ( A @ ( A @ p5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p5 ) )
!= ( C @ ( D @ p5 ) ) )
| ~ $true
| ~ ( B @ ( D @ p5 ) )
| ( C @ ( B @ p5 ) ) ),
inference(paramod_ordered,[status(thm)],[39,78]) ).
thf(209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ p5 ) )
!= ( C @ ( D @ p5 ) ) )
| ~ ( B @ ( D @ p5 ) )
| ( C @ ( B @ p5 ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( A @ ( B @ p5 ) ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p9 ) )
| ( B @ f15 @ ( A @ f15 @ p9 ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(35,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) )
| ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_35) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) )
| ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) )
| ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) )
!= ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) ) )
| ~ $true
| ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) ),
inference(paramod_ordered,[status(thm)],[77,89]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) )
!= ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) ) )
| ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f11 )
!= ( c24 @ f11 ) )
| ( ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) )
!= ( c28 @ f14 @ ( c27 @ f16 @ f13 ) ) )
| ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c24 )
| ( C
!= ( c28 @ f14 ) )
| ( ( C @ ( B @ ( A @ f19 ) ) )
!= ( c27 @ f16 ) )
| ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(178,plain,
! [A: $i] :
( ( ( c28 @ f14 @ ( A @ ( c24 @ f19 ) ) )
!= ( c27 @ f16 ) )
| ~ ( c24 @ f15 @ f11 @ ( c28 @ f14 @ ( A @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) )
!= ( c24 @ f15 @ f11 @ ( c28 @ f14 @ ( D @ f13 ) @ p23 ) ) )
| ( ( c28 @ f14 @ ( D @ ( c24 @ f19 ) ) )
!= ( c27 @ f16 ) )
| ~ $true
| ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) ),
inference(paramod_ordered,[status(thm)],[77,178]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) )
!= ( c24 @ f15 @ f11 @ ( c28 @ f14 @ ( D @ f13 ) @ p23 ) ) )
| ( ( c28 @ f14 @ ( D @ ( c24 @ f19 ) ) )
!= ( c27 @ f16 ) )
| ~ ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(184,plain,
! [A: $i] :
( ( ( c28 @ f14 @ ( c28 @ f14 @ ( A @ ( c24 @ f15 @ f19 ) ) @ ( c24 @ f19 ) ) )
!= ( c27 @ f16 ) )
| ~ ( c24 @ f15 @ f15 @ f11 @ ( c28 @ f14 @ ( A @ f13 ) @ p23 ) ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( c24 @ f15 )),bind(B,$thf( F )),bind(C,$thf( c28 @ f14 )),bind(D,$thf( c28 @ f14 @ ( F @ ( c24 @ f15 @ f19 ) ) ))]]) ).
thf(189,plain,
! [A: $i] :
( ( ( c28 @ f14 @ ( c28 @ f14 @ ( A @ ( c24 @ f15 @ f19 ) ) @ ( c24 @ f19 ) ) )
!= ( c27 @ f16 ) )
| ~ ( c24 @ f15 @ f15 @ f11 @ ( c28 @ f14 @ ( A @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(2,negated_conjecture,
! [A: $i] : ( A @ ( A @ p9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_2) ).
thf(46,plain,
! [A: $i] : ( A @ ( A @ p9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f20 @ ( A @ f20 @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_20) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f20 @ ( A @ f20 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p12 ) )
| ~ ( A @ ( C @ p12 ) )
| ( B @ ( A @ p12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_28) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p12 ) )
| ~ ( A @ ( C @ p12 ) )
| ( B @ ( A @ p12 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(36,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( c24 @ f11 @ ( B @ f14 @ ( A @ f13 ) @ p23 ) )
| ~ ( B @ ( c25 @ p22 ) )
| ( c26 @ f4 @ ( B @ ( A @ ( c26 @ f8 ) ) @ p21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_36) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( c24 @ f11 @ ( B @ f14 @ ( A @ f13 ) @ p23 ) )
| ~ ( B @ ( c25 @ p22 ) )
| ( c26 @ f4 @ ( B @ ( A @ ( c26 @ f8 ) ) @ p21 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ ( C @ p5 ) )
!= ( A @ ( C @ p5 ) ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
inference(eqfactor_ordered,[status(thm)],[78]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p5 ) )
| ( A @ ( A @ p5 ) ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( B ))]]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p5 ) )
| ( A @ ( A @ p5 ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(33,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f18 ) @ ( B @ ( A @ f18 ) @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_33) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f18 ) @ ( B @ ( A @ f18 ) @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(10,negated_conjecture,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ f18 ) @ f17 @ p5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_10) ).
thf(40,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ f18 ) @ f17 @ p5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ f18 ) @ f17 @ p5 ) )
!= ( D @ ( C @ p5 ) ) )
| ~ $true
| ( C @ ( D @ p5 ) ) ),
inference(paramod_ordered,[status(thm)],[40,210]) ).
thf(245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ f18 ) @ f17 @ p5 ) )
!= ( D @ ( C @ p5 ) ) )
| ( C @ ( D @ p5 ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(246,plain,
! [B: $i,A: $i] : ( B @ ( A @ f18 ) @ f17 @ ( A @ p5 ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ f18 ) @ f17 )),bind(D,$thf( F ))]]) ).
thf(260,plain,
! [B: $i,A: $i] : ( B @ ( A @ f18 ) @ f17 @ ( A @ p5 ) ),
inference(simp,[status(thm)],[246]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c24 @ f15 @ f11 @ ( c28 @ f14 @ ( c27 @ f13 ) @ p23 ) )
!= ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) )
| ~ $true
| ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) ) ),
inference(paramod_ordered,[status(thm)],[47,77]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c24 @ f15 @ f11 @ ( c28 @ f14 @ ( c27 @ f13 ) @ p23 ) )
!= ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) )
| ( A @ f11 @ ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(137,plain,
c24 @ f11 @ ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) @ p23 ),
inference(pattern_uni,[status(thm)],[136:[bind(A,$thf( c24 )),bind(B,$thf( c27 )),bind(C,$thf( c28 @ f14 ))]]) ).
thf(31,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p22 ) )
| ~ ( B @ ( D @ p6 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_31) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p22 ) )
| ~ ( B @ ( D @ p6 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p22 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p22 ) )
| ~ ( B @ ( D @ p6 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p22 ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(34,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ f15 @ f11 @ ( C @ ( A @ f13 ) @ p23 ) )
| ( C @ ( A @ ( B @ f19 ) ) @ ( c29 @ f20 @ f18 ) @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_34) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ f15 @ f11 @ ( C @ ( A @ f13 ) @ p23 ) )
| ( C @ ( A @ ( B @ f19 ) ) @ ( c29 @ f20 @ f18 ) @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(122,plain,
( ( ( c24 @ f15 )
!= c24 )
| ( ( c28 @ f14 )
!= ( c28 @ f14 ) )
| ( ( c27 @ f16 )
!= c27 ) ),
inference(simp,[status(thm)],[115]) ).
thf(124,plain,
( ( ( c24 @ f15 )
!= c24 )
| ( ( c27 @ f16 )
!= c27 ) ),
inference(simp,[status(thm)],[122]) ).
thf(140,plain,
( ( ( c24 @ f11 @ ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) @ p23 ) )
!= ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[137,89]) ).
thf(141,plain,
( ( c24 @ f11 @ ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) @ p23 ) )
!= ( c24 @ f11 @ ( c28 @ f14 @ ( c27 @ f16 @ f13 ) @ p23 ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(144,plain,
( ( ( c24 @ f11 )
!= ( c24 @ f11 ) )
| ( ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) )
!= ( c28 @ f14 @ ( c27 @ f16 @ f13 ) ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(146,plain,
( ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) )
!= ( c28 @ f14 @ ( c27 @ f16 @ f13 ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(147,plain,
( ( ( c28 @ f14 )
!= ( c28 @ f14 ) )
| ( ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) )
!= ( c27 @ f16 ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(148,plain,
( ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) )
!= ( c27 @ f16 ) ),
inference(simp,[status(thm)],[147]) ).
thf(32,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f13 ) @ ( B @ ( A @ f13 ) @ p12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_32) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f13 ) @ ( B @ ( A @ f13 ) @ p12 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(9,negated_conjecture,
c28 @ ( c25 @ p22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_9) ).
thf(44,plain,
c28 @ ( c25 @ p22 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p10 ) )
| ~ ( A @ ( C @ p10 ) )
| ( B @ ( A @ p10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_21) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p10 ) )
| ~ ( A @ ( C @ p10 ) )
| ( B @ ( A @ p10 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,negated_conjecture,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ f18 ) @ f16 @ p5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_11) ).
thf(50,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ f18 ) @ f16 @ p5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ f18 ) @ f16 @ p5 ) )
!= ( D @ ( C @ p5 ) ) )
| ~ $true
| ( C @ ( D @ p5 ) ) ),
inference(paramod_ordered,[status(thm)],[50,210]) ).
thf(242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ f18 ) @ f16 @ p5 ) )
!= ( D @ ( C @ p5 ) ) )
| ( C @ ( D @ p5 ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(243,plain,
! [B: $i,A: $i] : ( B @ ( A @ f18 ) @ f16 @ ( B @ p5 ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ f18 ) @ f16 )),bind(D,$thf( G ))]]) ).
thf(259,plain,
! [B: $i,A: $i] : ( B @ ( A @ f18 ) @ f16 @ ( B @ p5 ) ),
inference(simp,[status(thm)],[243]) ).
thf(24,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p6 ) )
| ~ ( A @ ( C @ p6 ) )
| ( B @ ( A @ p6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_24) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p6 ) )
| ~ ( A @ ( C @ p6 ) )
| ( B @ ( A @ p6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(18,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f16 @ ( A @ f16 @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_18) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f16 @ ( A @ f16 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f17 @ ( A @ f17 @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_19) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f17 @ ( A @ f17 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p5 ) )
!= ( C @ ( D @ p5 ) ) )
| ~ $true
| ( C @ ( C @ p5 ) )
| ~ ( B @ ( A @ p5 ) ) ),
inference(paramod_ordered,[status(thm)],[210,233]) ).
thf(317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ p5 ) )
!= ( C @ ( D @ p5 ) ) )
| ( C @ ( C @ p5 ) )
| ~ ( B @ ( A @ p5 ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ p5 ) )
| ~ ( B @ ( A @ p5 ) ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(7,negated_conjecture,
! [A: $i] : ( A @ ( A @ p2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_7) ).
thf(48,plain,
! [A: $i] : ( A @ ( A @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p6 ) )
| ( B @ f14 @ ( A @ f14 @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_17) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p6 ) )
| ( B @ f14 @ ( A @ f14 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_27) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(26,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_26) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c24 @ f11 @ ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) @ p23 ) )
!= ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) )
| ( ( A @ f11 )
!= ( c24 @ f11 ) )
| ( ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) )
!= ( c28 @ f14 @ ( c27 @ f16 @ f13 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[137,138]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c24 @ f11 @ ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) @ p23 ) )
!= ( A @ f15 @ f11 @ ( C @ ( B @ f13 ) @ p23 ) ) )
| ( ( A @ f11 )
!= ( c24 @ f11 ) )
| ( ( C @ ( C @ ( B @ ( A @ f19 ) ) @ f13 ) )
!= ( c28 @ f14 @ ( c27 @ f16 @ f13 ) ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ f15 @ f11 )
!= ( c24 @ f11 ) )
| ( ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) )
!= ( C @ ( B @ f13 ) ) )
| ( A != c24 )
| ( C
!= ( c28 @ f14 ) )
| ( ( C @ ( B @ ( A @ f19 ) ) )
!= ( c27 @ f16 ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(175,plain,
! [A: $i] :
( ( ( c24 @ f15 @ f11 )
!= ( c24 @ f11 ) )
| ( ( c28 @ f14 @ ( c28 @ f14 @ ( c27 @ ( c24 @ f19 ) ) @ f13 ) )
!= ( c28 @ f14 @ ( A @ f13 ) ) )
| ( ( c28 @ f14 @ ( A @ ( c24 @ f19 ) ) )
!= ( c27 @ f16 ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(6,negated_conjecture,
! [A: $i] : ( A @ ( A @ p3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_6) ).
thf(43,plain,
! [A: $i] : ( A @ ( A @ p3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ p2 ) )
| ~ ( F @ ( C @ p6 ) )
| ~ ( E @ ( B @ p5 ) )
| ( F @ ( E @ ( D @ f8 ) ) @ ( C @ ( B @ ( A @ f8 ) ) @ p7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_37) ).
thf(55,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ p2 ) )
| ~ ( F @ ( C @ p6 ) )
| ~ ( E @ ( B @ p5 ) )
| ( F @ ( E @ ( D @ f8 ) ) @ ( C @ ( B @ ( A @ f8 ) ) @ p7 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(30,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ p21 ) )
| ~ ( A @ ( D @ p7 ) )
| ~ ( B @ ( C @ p3 ) )
| ( B @ ( A @ p21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_30) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ p21 ) )
| ~ ( A @ ( D @ p7 ) )
| ~ ( B @ ( C @ p3 ) )
| ( B @ ( A @ p21 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(29,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ p10 ) )
| ~ ( D @ ( C @ p23 ) )
| ~ ( A @ ( C @ p12 ) )
| ( B @ ( A @ p23 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_29) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ p10 ) )
| ~ ( D @ ( C @ p23 ) )
| ~ ( A @ ( C @ p12 ) )
| ( B @ ( A @ p23 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p9 ) )
| ( B @ f11 @ ( A @ f11 @ p10 ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(8,negated_conjecture,
! [A: $i] : ( A @ ( A @ p12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_8) ).
thf(51,plain,
! [A: $i] : ( A @ ( A @ p12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,negated_conjecture,
! [A: $i] : ( A @ ( A @ p7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_3) ).
thf(68,plain,
! [A: $i] : ( A @ ( A @ p7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(38,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ p5 ) )
| ~ ( D @ ( A @ p9 ) )
| ~ ( F @ ( C @ p5 ) )
| ( F @ ( E @ ( D @ f19 ) ) @ ( C @ ( B @ ( A @ f19 ) ) @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_38) ).
thf(62,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ p5 ) )
| ~ ( D @ ( A @ p9 ) )
| ~ ( F @ ( C @ p5 ) )
| ( F @ ( E @ ( D @ f19 ) ) @ ( C @ ( B @ ( A @ f19 ) ) @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(14355,plain,
$false,
inference(e,[status(thm)],[115,56,42,52,121,53,41,73,66,80,123,210,83,69,138,189,46,57,78,61,89,74,233,60,260,70,137,92,65,124,77,148,45,64,44,59,259,71,54,49,76,318,39,48,63,50,67,72,175,43,40,55,75,58,82,146,51,47,68,62,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN631-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % 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
% 0.15/0.40 % Computer : n011.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 18:17:45 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 0.71/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.81 % [INFO] Parsing done (110ms).
% 0.94/0.82 % [INFO] Running in sequential loop mode.
% 1.20/1.01 % [INFO] eprover registered as external prover.
% 1.20/1.02 % [INFO] Scanning for conjecture ...
% 1.52/1.11 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.92/1.22 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.92/1.22 % [INFO] Problem is propositional (TPTP CNF).
% 1.92/1.22 % [INFO] Type checking passed.
% 1.92/1.23 % [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 ...
% 52.21/11.05 % External prover 'e' found a proof!
% 52.21/11.05 % [INFO] Killing All external provers ...
% 52.21/11.05 % Time passed: 10561ms (effective reasoning time: 10228ms)
% 52.21/11.05 % Axioms used in derivation (0):
% 52.21/11.05 % No. of inferences in proof: 131
% 52.21/11.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10561 ms resp. 10228 ms w/o parsing
% 43.59/11.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.59/11.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------