%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC003-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:29:53 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 52
% Syntax : Number of formulae : 129 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 832 ( 221 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 1306 ( 649 ~; 585 |; 0 &)
% ( 72 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 46 ( 46 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 199 ( 177 !; 0 ?; 199 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk7_type,type,
sk7: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
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,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(8,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[9,4]) ).
tff(11,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(13,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[13,10]) ).
tff(15,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(21,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(27,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(cons(sk5,nil),nil) = cons(sk5,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(cons(sk5,nil),nil) = cons(sk5,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(cons(sk5,nil),nil) = cons(sk5,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(cons(sk5,nil),nil) = cons(sk5,nil) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
app(cons(sk5,nil),nil) = cons(sk5,nil),
inference(unit_resolution,[status(thm)],[30,27,24,14]) ).
tff(32,plain,
( neq(app(cons(sk5,nil),nil),nil)
<=> neq(cons(sk5,nil),nil) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( neq(cons(sk5,nil),nil)
<=> neq(app(cons(sk5,nil),nil),nil) ),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ~ neq(cons(sk5,nil),nil)
<=> ~ neq(app(cons(sk5,nil),nil),nil) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(36,plain,
( ( ~ neq(sk4,nil)
| ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 ) )
<=> ( ~ neq(sk4,nil)
| ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
( ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
tff(39,plain,
( ~ neq(sk4,nil)
| ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ neq(sk4,nil)
| ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 ) ),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk4,
inference(unit_resolution,[status(thm)],[40,10]) ).
tff(42,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk2,
inference(transitivity,[status(thm)],[41,35]) ).
tff(43,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(45,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ neq(sk4,nil)
| ( app(sk6,sk7) = sk3 ) )
<=> ( ~ neq(sk4,nil)
| ( app(sk6,sk7) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ( app(sk6,sk7) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(sk6,sk7) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
( ( app(sk6,sk7) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_21) ).
tff(50,plain,
( ~ neq(sk4,nil)
| ( app(sk6,sk7) = sk3 ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ~ neq(sk4,nil)
| ( app(sk6,sk7) = sk3 ) ),
inference(modus_ponens,[status(thm)],[50,47]) ).
tff(52,plain,
app(sk6,sk7) = sk3,
inference(unit_resolution,[status(thm)],[51,10]) ).
tff(53,plain,
app(sk6,sk7) = sk1,
inference(transitivity,[status(thm)],[52,46]) ).
tff(54,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(60,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[66,27,63,14]) ).
tff(68,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 )
| ~ neq(B,nil) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 )
| ~ neq(B,nil) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 )
| ~ neq(B,nil) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 )
| ~ neq(B,nil) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 )
| ~ neq(B,nil)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 )
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 )
| ~ neq(B,nil)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 )
| ~ neq(B,nil)
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 )
| ~ neq(B,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(74,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ssList(sk7)
| ~ neq(sk4,nil) )
<=> ( ssList(sk7)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
tff(80,plain,
( ssList(sk7)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
ssList(sk7),
inference(unit_resolution,[status(thm)],[80,10]) ).
tff(82,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ( ssList(sk6)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(84,plain,
( ssList(sk6)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
ssList(sk6),
inference(unit_resolution,[status(thm)],[84,10]) ).
tff(86,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ~ ssList(sk7)
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) )
<=> ( ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(sk7)
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(sk7)
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(sk7)
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(B,nil)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ neq(cons(sk5,nil),nil)
| ( app(sk6,sk7) != sk1 )
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk2 ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
~ neq(cons(sk5,nil),nil),
inference(unit_resolution,[status(thm)],[91,10,85,81,77,67,53,42]) ).
tff(93,plain,
~ neq(app(cons(sk5,nil),nil),nil),
inference(modus_ponens,[status(thm)],[92,34]) ).
tff(94,plain,
( ssList(app(cons(sk5,nil),nil))
<=> ssList(cons(sk5,nil)) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(95,plain,
( ssList(cons(sk5,nil))
<=> ssList(app(cons(sk5,nil),nil)) ),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
ssList(app(cons(sk5,nil),nil)),
inference(modus_ponens,[status(thm)],[67,95]) ).
tff(97,plain,
( ( app(cons(sk5,nil),nil) = nil )
<=> ( cons(sk5,nil) = nil ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(98,plain,
( ( cons(sk5,nil) = nil )
<=> ( app(cons(sk5,nil),nil) = nil ) ),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ( cons(sk5,nil) != nil )
<=> ( app(cons(sk5,nil),nil) != nil ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(101,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( cons(U,V) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(106,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
cons(sk5,nil) != nil,
inference(unit_resolution,[status(thm)],[112,27,109,14]) ).
tff(114,plain,
app(cons(sk5,nil),nil) != nil,
inference(modus_ponens,[status(thm)],[113,99]) ).
tff(115,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(116,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)],[115]) ).
tff(117,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(118,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(119,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)],[118]) ).
tff(120,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(121,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(app(cons(sk5,nil),nil))
| ( app(cons(sk5,nil),nil) = nil )
| neq(app(cons(sk5,nil),nil),nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(app(cons(sk5,nil),nil))
| ( app(cons(sk5,nil),nil) = nil )
| neq(app(cons(sk5,nil),nil),nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(app(cons(sk5,nil),nil))
| ( app(cons(sk5,nil),nil) = nil )
| neq(app(cons(sk5,nil),nil),nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(app(cons(sk5,nil),nil))
| ( app(cons(sk5,nil),nil) = nil )
| neq(app(cons(sk5,nil),nil),nil) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
( ~ ssList(app(cons(sk5,nil),nil))
| ( app(cons(sk5,nil),nil) = nil )
| neq(app(cons(sk5,nil),nil),nil) ),
inference(unit_resolution,[status(thm)],[127,27,124]) ).
tff(129,plain,
$false,
inference(unit_resolution,[status(thm)],[128,114,96,93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC003-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:59:24 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.21/0.55 % SZS status Unsatisfiable
% 0.21/0.55 % SZS output start Proof
% See solution above
% 0.21/0.57 % E exiting
%------------------------------------------------------------------------------