%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC403-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:08 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 52
% Syntax : Number of formulae : 122 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 847 ( 49 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1299 ( 632 ~; 588 |; 0 &)
% ( 79 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 58 ( 58 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 250 ( 226 !; 0 ?; 250 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf47_type,type,
skaf47: ( $i * $i ) > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(skaf48_type,type,
skaf48: ( $i * $i ) > $i ).
tff(sk2_type,type,
sk2: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf47(U,V))
<=> ssList(skaf47(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ssList(skaf47(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf47(U,V)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ssList(skaf47(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf47(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause49) ).
tff(5,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf47(U,V))
| ssList(skaf47(sk4,sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ssList(skaf47(sk4,sk3)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(12,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(19,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ),
inference(unit_resolution,[status(thm)],[28,22,12]) ).
tff(30,plain,
ssList(app(skaf47(sk4,sk3),sk3)),
inference(unit_resolution,[status(thm)],[29,9]) ).
tff(31,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(33,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( segmentP(sk4,sk3)
<=> segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(37,plain,
segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
tff(40,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ segmentP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause168) ).
tff(47,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ ssList(sk4)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ ssList(sk4)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ ssList(sk4)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ ssList(sk4)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ ssList(sk4)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ ssList(sk4)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4,
inference(unit_resolution,[status(thm)],[56,50,12,40,37]) ).
tff(58,plain,
app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk2,
inference(transitivity,[status(thm)],[57,34]) ).
tff(59,plain,
( memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5)
<=> memberP(sk2,sk5) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( memberP(sk2,sk5)
<=> memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ memberP(sk2,sk5)
<=> ~ memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ~ memberP(sk2,sk5)
<=> ~ memberP(sk2,sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
~ memberP(sk2,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(64,plain,
~ memberP(sk2,sk5),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
~ memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5),
inference(modus_ponens,[status(thm)],[64,61]) ).
tff(66,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf48(U,V))
<=> ssList(skaf48(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [V: $i,U: $i] : ssList(skaf48(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf48(U,V)) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [V: $i,U: $i] : ssList(skaf48(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf48(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause48) ).
tff(70,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf48(U,V))
| ssList(skaf48(sk3,sk4)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
ssList(skaf48(sk3,sk4)),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(77,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ memberP(U,V)
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(W)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
tff(84,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
( ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(unit_resolution,[status(thm)],[93,87,77,74]) ).
tff(95,plain,
~ memberP(app(skaf47(sk4,sk3),sk3),sk5),
inference(unit_resolution,[status(thm)],[94,65,30]) ).
tff(96,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(98,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( memberP(sk3,sk5)
<=> memberP(sk1,sk5) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( memberP(sk1,sk5)
<=> memberP(sk3,sk5) ),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( memberP(sk1,sk5)
<=> memberP(sk1,sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
memberP(sk1,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(104,plain,
memberP(sk1,sk5),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
memberP(sk3,sk5),
inference(modus_ponens,[status(thm)],[104,101]) ).
tff(106,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ memberP(U,V)
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(U)
| ~ memberP(U,V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
tff(112,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ~ ssList(skaf47(sk4,sk3))
| memberP(app(skaf47(sk4,sk3),sk3),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ~ ssList(skaf47(sk4,sk3))
| memberP(app(skaf47(sk4,sk3),sk3),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ( ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ ssList(skaf47(sk4,sk3))
| ~ memberP(sk3,sk5)
| memberP(app(skaf47(sk4,sk3),sk3),sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ~ ssList(skaf47(sk4,sk3))
| memberP(app(skaf47(sk4,sk3),sk3),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ ssList(skaf47(sk4,sk3))
| ~ memberP(sk3,sk5)
| memberP(app(skaf47(sk4,sk3),sk3),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ~ ssList(skaf47(sk4,sk3))
| memberP(app(skaf47(sk4,sk3),sk3),sk5) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ ssList(skaf47(sk4,sk3))
| ~ memberP(sk3,sk5)
| memberP(app(skaf47(sk4,sk3),sk3),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ~ ssList(skaf47(sk4,sk3))
| memberP(app(skaf47(sk4,sk3),sk3),sk5) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ ssList(skaf47(sk4,sk3))
| ~ memberP(sk3,sk5)
| memberP(app(skaf47(sk4,sk3),sk3),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ~ ssList(skaf47(sk4,sk3))
| memberP(app(skaf47(sk4,sk3),sk3),sk5) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
$false,
inference(unit_resolution,[status(thm)],[121,115,12,77,105,9,95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC403-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 09:15:03 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.53 % SZS status Unsatisfiable
% 0.20/0.53 % SZS output start Proof
% See solution above
% 0.20/0.55 % E exiting
%------------------------------------------------------------------------------