%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC101-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:30:10 AM UTC 2025
% Result : Unsatisfiable 1.07s 1.31s
% Output : Proof 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 37
% Syntax : Number of formulae : 102 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 471 ( 118 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 632 ( 292 ~; 286 |; 0 &)
% ( 54 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 104 ( 93 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( nil = sk2 )
<=> ( nil = sk4 ) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( ( nil = sk4 )
<=> ( nil = sk2 ) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(7,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(9,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( neq(sk3,nil)
<=> neq(sk1,nil) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( neq(sk1,nil)
<=> neq(sk3,nil) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk3,nil) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(15,plain,
( ( app(sk3,sk5) = sk4 )
<=> ( app(sk3,sk5) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(17,plain,
app(sk3,sk5) = sk4,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(sk3,sk5) = sk2,
inference(transitivity,[status(thm)],[17,14]) ).
tff(19,plain,
( frontsegP(app(sk3,sk5),sk3)
<=> frontsegP(sk2,sk1) ),
inference(monotonicity,[status(thm)],[18,10]) ).
tff(20,plain,
( ssList(app(sk3,sk5))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(21,plain,
( ssList(sk4)
<=> ssList(app(sk3,sk5)) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(24,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
ssList(app(sk3,sk5)),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(28,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(31,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [V: $i,U: $i] :
rewrite(( ( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [W: $i,V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) )
<=> ! [V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(38,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) )
<=> ! [W: $i,V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(39,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) )
<=> ! [V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) ) ),
inference(transitivity,[status(thm)],[38,37]) ).
tff(40,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(transitivity,[status(thm)],[39,36]) ).
tff(41,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != W )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,axiom,
! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause144) ).
tff(45,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ),
inference(modus_ponens,[status(thm)],[45,34]) ).
tff(47,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ),
inference(modus_ponens,[status(thm)],[47,33]) ).
tff(49,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(app(sk3,sk5))
| frontsegP(app(sk3,sk5),sk3) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(app(sk3,sk5))
| frontsegP(app(sk3,sk5),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(app(sk3,sk5))
| frontsegP(app(sk3,sk5),sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(app(sk3,sk5))
| frontsegP(app(sk3,sk5),sk3) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ ssList(app(sk3,sk5))
| frontsegP(app(sk3,sk5),sk3) ),
inference(unit_resolution,[status(thm)],[51,48,31,28]) ).
tff(53,plain,
frontsegP(app(sk3,sk5),sk3),
inference(unit_resolution,[status(thm)],[52,25]) ).
tff(54,plain,
frontsegP(sk2,sk1),
inference(modus_ponens,[status(thm)],[53,19]) ).
tff(55,plain,
( ( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) )
<=> ( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(57,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[58,55]) ).
tff(60,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[60,55]) ).
tff(62,plain,
~ neq(sk1,nil),
inference(unit_resolution,[status(thm)],[61,54]) ).
tff(63,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[62,13]) ).
tff(64,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(70,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(76,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ( sk3 = nil )
| neq(sk3,nil) ),
inference(unit_resolution,[status(thm)],[79,76,73,31]) ).
tff(81,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[80,63]) ).
tff(82,plain,
nil = sk3,
inference(modus_ponens,[status(thm)],[81,6]) ).
tff(83,plain,
( ( ( nil = sk4 )
| ( nil != sk3 ) )
<=> ( ( nil = sk4 )
| ( nil != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,axiom,
( ( nil = sk4 )
| ( nil != sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(85,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[85,83]) ).
tff(87,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[86,83]) ).
tff(88,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[88,83]) ).
tff(90,plain,
nil = sk4,
inference(unit_resolution,[status(thm)],[89,82]) ).
tff(91,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[90,5]) ).
tff(92,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(93,plain,
( ( nil = sk3 )
<=> ( nil = sk1 ) ),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ( sk3 = nil )
<=> ( nil = sk1 ) ),
inference(transitivity,[status(thm)],[6,93]) ).
tff(95,plain,
nil = sk1,
inference(modus_ponens,[status(thm)],[81,94]) ).
tff(96,plain,
( ( ( nil != sk1 )
| ( nil != sk2 ) )
<=> ( ( nil != sk1 )
| ( nil != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ( ( nil != sk2 )
| ( nil != sk1 ) )
<=> ( ( nil != sk1 )
| ( nil != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(99,plain,
( ( nil != sk1 )
| ( nil != sk2 ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ( nil != sk1 )
| ( nil != sk2 ) ),
inference(modus_ponens,[status(thm)],[99,96]) ).
tff(101,plain,
nil != sk2,
inference(unit_resolution,[status(thm)],[100,95]) ).
tff(102,plain,
$false,
inference(unit_resolution,[status(thm)],[101,91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC101-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:21:27 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.07/1.31 % SZS status Unsatisfiable
% 1.07/1.31 % SZS output start Proof
% See solution above
% 1.14/1.32 % E exiting
%------------------------------------------------------------------------------