%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV191+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 : n016.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 09:01:36 AM UTC 2026
% Result : Theorem 14.62s 3.93s
% Output : CNFRefutation 14.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 117 ( 64 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 99 ( 15 ~; 15 |; 61 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 16 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(gt_0_tptp_minus_1,axiom,
gt(n0,'tptp$uminus$u1') ).
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(transitivity_leq,axiom,
! [X0,X1,X2] :
( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ).
fof(leq_gt2,axiom,
! [X0,X1] :
( ( X0 != X1
& leq(X0,X1) )
=> gt(X1,X0) ) ).
fof(leq_gt_pred,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ) ).
fof(gt_succ,axiom,
! [X0] : gt(succ(X0),X0) ).
fof(succ_tptp_minus_1,axiom,
succ('tptp$uminus$u1') = n0 ).
fof(quaternion_ds1_inuse_0002,conjecture,
( ( 'a$uselect2'('xinit$unoise$udefuse',n5) = use
& 'a$uselect2'('xinit$unoise$udefuse',n4) = use
& 'a$uselect2'('xinit$unoise$udefuse',n3) = use
& 'a$uselect2'('xinit$unoise$udefuse',n2) = use
& 'a$uselect2'('xinit$unoise$udefuse',n1) = use
& 'a$uselect2'('xinit$unoise$udefuse',n0) = use
& 'a$uselect2'('xinit$umean$udefuse',n5) = use
& 'a$uselect2'('xinit$umean$udefuse',n4) = use
& 'a$uselect2'('xinit$umean$udefuse',n3) = use
& 'a$uselect2'('xinit$umean$udefuse',n2) = use
& 'a$uselect2'('xinit$umean$udefuse',n1) = use
& 'a$uselect2'('xinit$umean$udefuse',n0) = use
& '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$uselect2'('sigma$udefuse',n5) = use
& 'a$uselect2'('sigma$udefuse',n4) = use
& 'a$uselect2'('sigma$udefuse',n3) = use
& 'a$uselect2'('sigma$udefuse',n2) = use
& 'a$uselect2'('sigma$udefuse',n1) = use
& 'a$uselect2'('sigma$udefuse',n0) = use
& 'a$uselect2'('rho$udefuse',n2) = use
& 'a$uselect2'('rho$udefuse',n1) = use
& 'a$uselect2'('rho$udefuse',n0) = use )
=> ! [X0,X1] :
( ( leq(X1,'tptp$uminus$u1')
& leq(X0,n2)
& leq(n0,X1)
& leq(n0,X0) )
=> 'a$uselect3'('z$udefuse',X0,X1) = use ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( 'a$uselect2'('xinit$unoise$udefuse',n5) = use
& 'a$uselect2'('xinit$unoise$udefuse',n4) = use
& 'a$uselect2'('xinit$unoise$udefuse',n3) = use
& 'a$uselect2'('xinit$unoise$udefuse',n2) = use
& 'a$uselect2'('xinit$unoise$udefuse',n1) = use
& 'a$uselect2'('xinit$unoise$udefuse',n0) = use
& 'a$uselect2'('xinit$umean$udefuse',n5) = use
& 'a$uselect2'('xinit$umean$udefuse',n4) = use
& 'a$uselect2'('xinit$umean$udefuse',n3) = use
& 'a$uselect2'('xinit$umean$udefuse',n2) = use
& 'a$uselect2'('xinit$umean$udefuse',n1) = use
& 'a$uselect2'('xinit$umean$udefuse',n0) = use
& '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$uselect2'('sigma$udefuse',n5) = use
& 'a$uselect2'('sigma$udefuse',n4) = use
& 'a$uselect2'('sigma$udefuse',n3) = use
& 'a$uselect2'('sigma$udefuse',n2) = use
& 'a$uselect2'('sigma$udefuse',n1) = use
& 'a$uselect2'('sigma$udefuse',n0) = use
& 'a$uselect2'('rho$udefuse',n2) = use
& 'a$uselect2'('rho$udefuse',n1) = use
& 'a$uselect2'('rho$udefuse',n0) = use )
=> ! [X0,X1] :
( ( leq(X1,'tptp$uminus$u1')
& leq(X0,n2)
& leq(n0,X1)
& leq(n0,X0) )
=> 'a$uselect3'('z$udefuse',X0,X1) = use ) ),
inference(negate_conjecture,[status(cth)],[quaternion_ds1_inuse_0002]) ).
cnf(c3,plain,
gt(n0,'tptp$uminus$u1'),
inference(clausification,[status(esa)],[gt_0_tptp_minus_1]) ).
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(c36,plain,
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_leq]) ).
cnf(c42,plain,
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[leq_gt2]) ).
cnf(c43,plain,
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(clausification,[status(esa)],[leq_gt_pred]) ).
cnf(c44,plain,
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(clausification,[status(esa)],[leq_gt_pred]) ).
cnf(c45,plain,
gt(succ(X0),X0),
inference(clausification,[status(esa)],[gt_succ]) ).
cnf(c123,plain,
succ('tptp$uminus$u1') = n0,
inference(clausification,[status(esa)],[succ_tptp_minus_1]) ).
cnf(c184,plain,
leq(n0,sK182),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c186,plain,
leq(sK182,'tptp$uminus$u1'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( gt('tptp$uminus$u1',sK182)
| sK182 = 'tptp$uminus$u1' ),
inference(resolution,[status(thm)],[c42,c186]) ).
cnf(d1,plain,
( leq(n0,X0)
| ~ leq(sK182,X0) ),
inference(resolution,[status(thm)],[c36,c184]) ).
cnf(d2,plain,
( leq(n0,pred(X0))
| ~ gt(X0,sK182) ),
inference(resolution,[status(thm)],[c44,d1]) ).
cnf(d3,plain,
( gt(X0,n0)
| ~ gt(X0,sK182) ),
inference(resolution,[status(thm)],[d2,c43]) ).
cnf(d4,plain,
( sK182 = 'tptp$uminus$u1'
| gt('tptp$uminus$u1',n0) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( gt(n0,X0)
| ~ gt('tptp$uminus$u1',X0) ),
inference(resolution,[status(thm)],[c33,c3]) ).
cnf(d6,plain,
( sK182 = 'tptp$uminus$u1'
| gt(n0,n0) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
sK182 = 'tptp$uminus$u1',
inference(resolution,[status(thm)],[c34,d6]) ).
cnf(d8,plain,
gt(succ(sK182),n0),
inference(resolution,[status(thm)],[d3,c45]) ).
cnf(d9,plain,
gt(succ('tptp$uminus$u1'),n0),
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
gt(n0,n0),
inference(demodulation,[status(thm)],[d9,c123]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c34,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV191+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
% 0.09/0.34 % Computer : n016.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 13:23:45 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.62/3.93 % SZS status Theorem for theBenchmark.p
% 14.62/3.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------