%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:31:11 AM UTC 2026
% Result : Unsatisfiable 47.49s 11.27s
% Output : Refutation 39.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 104 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 340 ( 112 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1802 ( 196 ~; 180 |; 0 &;1426 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 210 ( 0 ^; 210 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_Y_decl,type,
v_Y: $i ).
thf(c_Zorn_OTFin_decl,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(v_S_decl,type,
v_S: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_n_decl,type,
v_n: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_Zorn_Osucc_decl,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Zorn_OTFin__linear__lemma1__1_decl,type,
c_Zorn_OTFin__linear__lemma1__1: $i > $i > $i > $i ).
thf(1,negated_conjecture,
t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(16,plain,
t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
~ ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(20,plain,
~ ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
~ ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(41,plain,
( ( ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,21]) ).
thf(42,plain,
( ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
( ( ( t_a @ tc_set @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y ) ),
inference(simp,[status(thm)],[42]) ).
thf(47,plain,
( ( ( t_a @ tc_set @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y ) ),
inference(simp,[status(thm)],[43]) ).
thf(56,plain,
( ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y ) ),
inference(simp,[status(thm)],[47]) ).
thf(6,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( t_a @ tc_set @ tc_set @ ( B @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( t_a @ tc_set @ tc_set @ ( B @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( t_a @ tc_set @ tc_set @ ( B @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( t_a @ tc_set @ tc_set @ ( B @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( B != v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( A @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y )
| ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( t_a @ tc_set @ tc_set @ ( B @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,56]) ).
thf(74,plain,
! [A: $i] :
( ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( A @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y )
| ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( v_S @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_S @ ( A @ c_lessequals ) ) )
| ( t_a @ tc_set @ tc_set @ ( v_S @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( A )),bind(B,$thf( v_S ))]]) ).
thf(3,negated_conjecture,
t_a @ tc_set @ tc_set @ ( v_Y @ ( v_x @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(19,plain,
t_a @ tc_set @ tc_set @ ( v_Y @ ( v_x @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ tc_set @ ( v_Y @ ( v_x @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,26]) ).
thf(888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ tc_set @ ( v_Y @ ( v_x @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[887]) ).
thf(889,plain,
! [A: $i] :
( ( t_a @ tc_set @ tc_set @ ( A @ ( v_x @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[888:[bind(A,$thf( v_x )),bind(B,$thf( v_Y )),bind(C,$thf( t_a @ tc_set @ tc_set )),bind(D,$thf( D ))]]) ).
thf(920,plain,
! [A: $i] :
( ( t_a @ tc_set @ tc_set @ ( A @ ( v_x @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[889]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(1796,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( F @ ( E @ ( F @ ( E @ ( D @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) )
| ( F @ tc_set @ ( E @ ( D @ c_lessequals ) ) )
| ~ $true
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,30]) ).
thf(1797,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( F @ ( E @ ( F @ ( E @ ( D @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) )
| ( F @ tc_set @ ( E @ ( D @ c_lessequals ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1796]) ).
thf(1798,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
| ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[1797:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(1824,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1798]) ).
thf(5,negated_conjecture,
~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(15,plain,
~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
~ ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1824,24]) ).
thf(1831,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1856,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( A != v_x )
| ( A
!= ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) ) ) ),
inference(simp,[status(thm)],[1831]) ).
thf(1858,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x ) ),
inference(simp,[status(thm)],[1856]) ).
thf(1902,plain,
! [A: $i] :
( ( A
!= ( t_a @ tc_set ) )
| ( ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x ) ),
inference(simp,[status(thm)],[1858]) ).
thf(1942,plain,
( ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x ),
inference(simp,[status(thm)],[1902]) ).
thf(44,plain,
( ( ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,24]) ).
thf(45,plain,
( ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
( ( ( t_a @ tc_set @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= v_x )
| ( ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_Y ) ),
inference(simp,[status(thm)],[45]) ).
thf(659,plain,
( ( ( t_a @ tc_set @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= v_x )
| ( ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_Y ) ),
inference(simp,[status(thm)],[46]) ).
thf(718,plain,
( ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ c_Zorn_OTFin ) )
!= v_x )
| ( ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_Y ) ),
inference(simp,[status(thm)],[659]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( A @ ( C @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( A @ ( C @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2,negated_conjecture,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_n @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(18,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_n @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1838,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1824,21]) ).
thf(1839,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1857,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( A != v_n )
| ( A != v_x ) ),
inference(simp,[status(thm)],[1839]) ).
thf(1859,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( v_x != v_n ) ),
inference(simp,[status(thm)],[1857]) ).
thf(1863,plain,
! [A: $i] :
( ( A
!= ( t_a @ tc_set ) )
| ( v_x != v_n ) ),
inference(simp,[status(thm)],[1859]) ).
thf(1887,plain,
v_x != v_n,
inference(simp,[status(thm)],[1863]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,24]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_x @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) )
!= v_x )
| ( A
!= ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( B @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ ( A @ c_Zorn_Osucc ) ) )
!= v_x ) ),
inference(simp,[status(thm)],[52]) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ ( A @ c_Zorn_Osucc ) ) )
!= v_x ) ),
inference(simp,[status(thm)],[54]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1171,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set @ ( v_S @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ) )
| ~ $true
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( A @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y )
| ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( v_S @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_S @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[74,21]) ).
thf(1172,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set @ ( v_S @ ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ) )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( A @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y )
| ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( v_S @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_S @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1171]) ).
thf(1324,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( v_n != v_S )
| ( ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( A @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y )
| ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( v_S @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_S @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1356,plain,
! [A: $i] :
( ( v_n != v_S )
| ( ( t_a @ ( A @ ( v_S @ c_Zorn_Osucc ) ) )
!= v_x )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( A @ c_Zorn_OTFin ) )
!= v_n )
| ( v_x != v_Y )
| ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( v_S @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_S @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1324]) ).
thf(890,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( F @ ( E @ ( D @ c_in ) ) ) )
| ( F @ ( G @ ( D @ c_in ) ) )
| ~ ( F @ tc_set @ ( G @ ( E @ c_lessequals ) ) )
| ~ $true
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,26]) ).
thf(891,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( F @ ( E @ ( D @ c_in ) ) ) )
| ( F @ ( G @ ( D @ c_in ) ) )
| ~ ( F @ tc_set @ ( G @ ( E @ c_lessequals ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[890]) ).
thf(892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( D @ ( C @ ( B @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[891:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( J @ ( I @ ( H @ c_Main_OsubsetI__1 ) ) )),bind(E,$thf( H )),bind(F,$thf( J ))]]) ).
thf(922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( D @ ( C @ ( B @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[892]) ).
thf(1626,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) )
!= ( D @ tc_set @ ( A @ ( B @ c_lessequals ) ) ) )
| ( D @ ( A @ ( D @ ( C @ ( B @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
| ~ $true
| ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,922]) ).
thf(1627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) )
!= ( D @ tc_set @ ( A @ ( B @ c_lessequals ) ) ) )
| ( D @ ( A @ ( D @ ( C @ ( B @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
| ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1626]) ).
thf(1628,plain,
! [A: $i] :
( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( t_a @ tc_set @ tc_set @ ( A @ ( v_Y @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[1627:[bind(A,$thf( t_a @ ( v_S @ c_Zorn_OTFin ) )),bind(B,$thf( v_Y )),bind(C,$thf( C )),bind(D,$thf( t_a @ tc_set @ tc_set ))]]) ).
thf(1667,plain,
! [A: $i] :
( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( t_a @ tc_set @ tc_set @ ( A @ ( v_Y @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1628]) ).
thf(893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) )
!= ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ $true
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,26]) ).
thf(894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) )
!= ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[893]) ).
thf(895,plain,
! [A: $i] :
( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( v_Y @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[894:[bind(A,$thf( A )),bind(B,$thf( v_Y )),bind(C,$thf( t_a @ tc_set @ tc_set )),bind(D,$thf( t_a @ ( v_S @ c_Zorn_OTFin ) ))]]) ).
thf(834,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( ( B @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ ( A @ c_Zorn_Osucc ) ) )
!= v_x ) ),
inference(simp,[status(thm)],[598]) ).
thf(868,plain,
! [A: $i] :
( ( t_a @ ( t_a @ ( v_n @ ( v_S @ c_Zorn_Osucc ) ) @ ( A @ c_Zorn_Osucc ) ) )
!= v_x ),
inference(simp,[status(thm)],[834]) ).
thf(964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ tc_set @ ( D @ ( v_Y @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( D @ ( v_x @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,920]) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ tc_set @ ( D @ ( v_Y @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( D @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[964]) ).
thf(966,plain,
! [A: $i] : ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_Y @ ( A @ c_Zorn_Osucc ) ) @ ( v_x @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[965:[bind(A,$thf( v_Y )),bind(B,$thf( E )),bind(C,$thf( t_a @ tc_set )),bind(D,$thf( t_a @ tc_set @ ( v_Y @ ( E @ c_Zorn_Osucc ) ) ))]]) ).
thf(1015,plain,
! [A: $i] : ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_Y @ ( A @ c_Zorn_Osucc ) ) @ ( v_x @ c_in ) ) ),
inference(simp,[status(thm)],[966]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,21]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_x @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) )
!= v_n )
| ( A != v_x ) ),
inference(simp,[status(thm)],[51]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set )
!= ( t_a @ tc_set @ tc_set ) )
| ( ( B @ ( v_x @ ( A @ c_Zorn_Osucc ) ) )
!= v_n ) ),
inference(simp,[status(thm)],[53]) ).
thf(505,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ ( v_x @ ( A @ c_Zorn_Osucc ) ) )
!= v_n ) ),
inference(simp,[status(thm)],[55]) ).
thf(548,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( ( B @ ( v_x @ ( A @ c_Zorn_Osucc ) ) )
!= v_n ) ),
inference(simp,[status(thm)],[505]) ).
thf(571,plain,
! [A: $i] :
( ( t_a @ ( v_x @ ( A @ c_Zorn_Osucc ) ) )
!= v_n ),
inference(simp,[status(thm)],[548]) ).
thf(961,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_x @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,920]) ).
thf(962,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_Y @ c_lessequals ) ) )
!= ( t_a @ tc_set @ tc_set @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[961]) ).
thf(963,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_x @ c_in ) ),
inference(pattern_uni,[status(thm)],[962:[bind(A,$thf( t_a @ ( v_S @ c_Zorn_OTFin ) ))]]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) )
!= A )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) )
!= A )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5216,plain,
$false,
inference(e,[status(thm)],[56,74,920,1942,718,27,39,18,659,24,25,1887,20,46,29,28,598,1824,21,17,32,34,54,1356,1667,895,868,1015,505,922,16,31,571,43,963,26,55,23,36,30,19,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.23/0.48 % Computer : n020.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sat Sep 26 08:22:49 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 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
% 1.44/1.30 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.59 % [INFO] Parsing done (276ms).
% 2.07/1.61 % [INFO] Running in sequential loop mode.
% 2.87/2.12 % [INFO] eprover registered as external prover.
% 2.87/2.12 % [INFO] Scanning for conjecture ...
% 3.22/2.24 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 3.22/2.29 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.41/2.32 % [INFO] Problem is propositional (TPTP CNF).
% 3.41/2.32 % [INFO] Type checking passed.
% 3.41/2.32 % [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 ...
% 47.49/11.26 % External prover 'e' found a proof!
% 47.49/11.27 % [INFO] Killing All external provers ...
% 47.49/11.27 % Time passed: 10583ms (effective reasoning time: 9653ms)
% 47.49/11.27 % Axioms used in derivation (8): cls_Set_OsubsetI_1, cls_Zorn_OTFin__linear__lemma1_0, cls_Set_OsubsetI_0, cls_Zorn_OTFin__linear__lemma1_3, cls_Set_OsubsetD_0, cls_Zorn_OTFin__linear__lemma1_2, cls_Zorn_OAbrial__axiom1_0, cls_Zorn_OTFin__linear__lemma1_1
% 47.49/11.27 % No. of inferences in proof: 104
% 47.49/11.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10583 ms resp. 9653 ms w/o parsing
% 39.81/11.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.81/11.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------