%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC009-1 : 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 05:29:54 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 56 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 263 ( 106 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 396 ( 204 ~; 168 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 68 ( 61 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $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,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(7,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(sk4,nil) = sk4,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
( ( app(sk3,sk5) = sk4 )
<=> ( app(sk3,sk5) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(21,plain,
app(sk3,sk5) = sk4,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
app(app(sk3,sk5),nil) = app(sk4,nil),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
app(app(sk3,sk5),nil) = sk2,
inference(transitivity,[status(thm)],[22,18,4]) ).
tff(24,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(26,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(30,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[33,14,30]) ).
tff(35,plain,
app(sk3,nil) = sk1,
inference(transitivity,[status(thm)],[34,27]) ).
tff(36,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(38,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [B: $i,A: $i,C: $i] :
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 ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(45,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(51,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,sk5),nil) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,sk5),nil) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,sk5),nil) != sk2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,sk5),nil) != sk2 ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
app(app(sk3,sk5),nil) != sk2,
inference(unit_resolution,[status(thm)],[54,51,30,48,38,35]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC009-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:59:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------