%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV104+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 09:01:26 AM UTC 2026
% Result : Theorem 58.08s 7.82s
% Output : CNFRefutation 58.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 34 unt; 0 def)
% Number of atoms : 150 ( 122 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 153 ( 62 ~; 64 |; 22 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 40 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(gt_5_4,axiom,
gt(n5,n4) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4 ).
fof(successor_1,axiom,
succ(n0) = n1 ).
fof(successor_2,axiom,
succ(succ(n0)) = n2 ).
fof(successor_3,axiom,
succ(succ(succ(n0))) = n3 ).
fof(transitivity_gt,axiom,
! [X0,X1,X2] :
( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ) ).
fof(irreflexivity_gt,axiom,
! [X0] : ~ gt(X0,X0) ).
fof(reflexivity_leq,axiom,
! [X0] : leq(X0,X0) ).
fof(gt_succ,axiom,
! [X0] : gt(succ(X0),X0) ).
fof(leq_succ_gt_equiv,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ) ).
fof(sel2_update_1,axiom,
! [X0,X1,X2] : 'a$uselect2'('tptp$uupdate2'(X0,X1,X2),X1) = X2 ).
fof(sel2_update_2,axiom,
! [X0,X1,X2,X3,X4] :
( ( 'a$uselect2'(X2,X1) = X3
& X0 != X1 )
=> 'a$uselect2'('tptp$uupdate2'(X2,X0,X4),X1) = X3 ) ).
fof(quaternion_ds1_inuse_0016,conjecture,
( ( 'a$uselect2'('xinit$udefuse',n5) = use
& 'a$uselect2'('xinit$udefuse',n4) = use
& 'a$uselect2'('xinit$udefuse',n3) = use
& 'a$uselect3'('u$udefuse',n2,n0) = use
& 'a$uselect3'('u$udefuse',n1,n0) = use
& 'a$uselect3'('u$udefuse',n0,n0) = use )
=> ( 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n5) = use
& 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n4) = use
& 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n3) = use
& 'a$uselect3'('u$udefuse',n2,n0) = use
& 'a$uselect3'('u$udefuse',n1,n0) = use
& 'a$uselect3'('u$udefuse',n0,n0) = use ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( 'a$uselect2'('xinit$udefuse',n5) = use
& 'a$uselect2'('xinit$udefuse',n4) = use
& 'a$uselect2'('xinit$udefuse',n3) = use
& 'a$uselect3'('u$udefuse',n2,n0) = use
& 'a$uselect3'('u$udefuse',n1,n0) = use
& 'a$uselect3'('u$udefuse',n0,n0) = use )
=> ( 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n5) = use
& 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n4) = use
& 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n3) = use
& 'a$uselect3'('u$udefuse',n2,n0) = use
& 'a$uselect3'('u$udefuse',n1,n0) = use
& 'a$uselect3'('u$udefuse',n0,n0) = use ) ),
inference(negate_conjecture,[status(cth)],[quaternion_ds1_inuse_0016]) ).
cnf(c0,plain,
gt(n5,n4),
inference(clausification,[status(esa)],[gt_5_4]) ).
cnf(c27,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(clausification,[status(esa)],[successor_4]) ).
cnf(c29,plain,
succ(n0) = n1,
inference(clausification,[status(esa)],[successor_1]) ).
cnf(c30,plain,
succ(succ(n0)) = n2,
inference(clausification,[status(esa)],[successor_2]) ).
cnf(c31,plain,
succ(succ(succ(n0))) = n3,
inference(clausification,[status(esa)],[successor_3]) ).
cnf(c33,plain,
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_gt]) ).
cnf(c34,plain,
~ gt(X0,X0),
inference(clausification,[status(esa)],[irreflexivity_gt]) ).
cnf(c35,plain,
leq(X0,X0),
inference(clausification,[status(esa)],[reflexivity_leq]) ).
cnf(c45,plain,
gt(succ(X0),X0),
inference(clausification,[status(esa)],[gt_succ]) ).
cnf(c47,plain,
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[leq_succ_gt_equiv]) ).
cnf(c149,plain,
'a$uselect2'('tptp$uupdate2'(X0,X1,X2),X1) = X2,
inference(clausification,[status(esa)],[sel2_update_1]) ).
cnf(c150,plain,
( 'a$uselect2'('tptp$uupdate2'(X2,X0,X4),X1) = X3
| 'a$uselect2'(X2,X1) != X3
| X0 = X1 ),
inference(clausification,[status(esa)],[sel2_update_2]) ).
cnf(c156,plain,
'a$uselect3'('u$udefuse',n0,n0) = use,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c157,plain,
'a$uselect3'('u$udefuse',n1,n0) = use,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c158,plain,
'a$uselect3'('u$udefuse',n2,n0) = use,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c162,plain,
( 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n5) != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n3) != use
| 'a$uselect3'('u$udefuse',n2,n0) != use
| 'a$uselect3'('u$udefuse',n0,n0) != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n4) != use
| 'a$uselect3'('u$udefuse',n1,n0) != use ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'a$uselect3'('u$udefuse',n2,n0) != use
| 'a$uselect3'('u$udefuse',n1,n0) != use
| 'a$uselect3'('u$udefuse',n0,n0) != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n3) != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n4) != use
| use != use ),
inference(demodulation,[status(thm)],[c162,c149]) ).
cnf(d1,plain,
( 'a$uselect3'('u$udefuse',n2,n0) != use
| 'a$uselect3'('u$udefuse',n1,n0) != use
| use != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n3) != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n4) != use
| use != use ),
inference(demodulation,[status(thm)],[d0,c156]) ).
cnf(d2,plain,
( 'a$uselect3'('u$udefuse',n2,n0) != use
| use != use
| use != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n3) != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n4) != use
| use != use ),
inference(demodulation,[status(thm)],[d1,c157]) ).
cnf(d3,plain,
( use != use
| use != use
| use != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n3) != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n4) != use
| use != use ),
inference(demodulation,[status(thm)],[d2,c158]) ).
cnf(d4,plain,
( 'a$uselect2'('tptp$uupdate2'(X2,X0,X3),X1) = 'a$uselect2'(X2,X1)
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c150]) ).
cnf(d5,plain,
( n5 = n3
| use != use
| use != use
| use != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n5,use),n4) != use
| use != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n3) != use ),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( n5 = n4
| use != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n3) != use
| n5 = n3
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n4) != use ),
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d7,plain,
( use != use
| 'a$uselect2'('tptp$uupdate2'('tptp$uupdate2'('xinit$udefuse',n3,use),n4,use),n3) != use
| use != use
| n5 = n3
| n5 = n4 ),
inference(demodulation,[status(thm)],[d6,c149]) ).
cnf(d8,plain,
( n4 = n3
| use != use
| use != use
| n5 = n3
| n5 = n4
| 'a$uselect2'('tptp$uupdate2'('xinit$udefuse',n3,use),n3) != use ),
inference(superposition,[status(thm)],[d4,d7]) ).
cnf(d9,plain,
( use != use
| use != use
| n4 = n3
| n5 = n3
| n5 = n4 ),
inference(demodulation,[status(thm)],[d8,c149]) ).
cnf(d10,plain,
( use != use
| n4 = n3
| n5 = n3
| n5 = n4 ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( n4 = n3
| n5 = n3
| n5 = n4 ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( n4 = n3
| n5 = n3
| gt(n4,n4) ),
inference(superposition,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
( n4 = n3
| n5 = n3 ),
inference(resolution,[status(thm)],[c34,d12]) ).
cnf(d14,plain,
( n4 = n3
| gt(n3,n4) ),
inference(superposition,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
( gt(succ(X0),X1)
| ~ gt(X0,X1) ),
inference(resolution,[status(thm)],[c33,c45]) ).
cnf(d16,plain,
~ gt(X0,succ(X0)),
inference(resolution,[status(thm)],[d15,c34]) ).
cnf(d17,plain,
succ(n1) = n2,
inference(demodulation,[status(thm)],[c30,c29]) ).
cnf(d18,plain,
succ(succ(n1)) = n3,
inference(demodulation,[status(thm)],[c31,c29]) ).
cnf(d19,plain,
succ(n2) = n3,
inference(demodulation,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
succ(succ(succ(n1))) = n4,
inference(demodulation,[status(thm)],[c27,c29]) ).
cnf(d21,plain,
succ(succ(n2)) = n4,
inference(demodulation,[status(thm)],[d20,d17]) ).
cnf(d22,plain,
succ(n3) = n4,
inference(demodulation,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
~ gt(n3,n4),
inference(superposition,[status(thm)],[d22,d16]) ).
cnf(d24,plain,
n4 = n3,
inference(resolution,[status(thm)],[d23,d14]) ).
cnf(d25,plain,
~ leq(succ(X0),X0),
inference(resolution,[status(thm)],[c47,c34]) ).
cnf(d26,plain,
~ leq(n4,n3),
inference(superposition,[status(thm)],[d22,d25]) ).
cnf(d27,plain,
~ leq(n3,n3),
inference(demodulation,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[c35,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV104+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:14:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.08/7.82 % SZS status Theorem for theBenchmark.p
% 58.08/7.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------