%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG226+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 06:48:10 AM UTC 2026
% Result : Theorem 16.00s 20.01s
% Output : CNFRefutation 16.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 65 ( 18 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 56 ( 19 ~; 18 |; 8 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_closure3,axiom,
! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( ( 'm1$upboole'(X1,X0)
& 'v2$urelat$u1'(X1) )
=> X1 = 'k1$ufunct$u4'('k1$upboole'(X0),'k7$urelat$u1'(X1,'k1$uclosure3'(X0,X1))) ) ) ).
fof(reflexivity_r6_pboole,axiom,
! [X0,X1,X2] :
( ( 'm1$upboole'(X2,X0)
& 'm1$upboole'(X1,X0) )
=> 'r6$upboole'(X0,X1,X1) ) ).
fof(t7_closure3,conjecture,
! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( ( 'm1$upboole'(X1,X0)
& 'v2$urelat$u1'(X1) )
=> ! [X2] :
( ( 'm1$upboole'(X2,X0)
& 'v2$urelat$u1'(X2) )
=> ( ( 'k7$urelat$u1'(X1,'k1$uclosure3'(X0,X1)) = 'k7$urelat$u1'(X2,'k1$uclosure3'(X0,X2))
& 'k1$uclosure3'(X0,X1) = 'k1$uclosure3'(X0,X2) )
=> 'r6$upboole'(X0,X1,X2) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( ( 'm1$upboole'(X1,X0)
& 'v2$urelat$u1'(X1) )
=> ! [X2] :
( ( 'm1$upboole'(X2,X0)
& 'v2$urelat$u1'(X2) )
=> ( ( 'k7$urelat$u1'(X1,'k1$uclosure3'(X0,X1)) = 'k7$urelat$u1'(X2,'k1$uclosure3'(X0,X2))
& 'k1$uclosure3'(X0,X1) = 'k1$uclosure3'(X0,X2) )
=> 'r6$upboole'(X0,X1,X2) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t7_closure3]) ).
cnf(c2,plain,
( 'k1$ufunct$u4'('k1$upboole'(X0),'k7$urelat$u1'(X1,'k1$uclosure3'(X0,X1))) = X1
| ~ 'v2$urelat$u1'(X1)
| ~ 'm1$upboole'(X1,X0)
| 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[t6_closure3]) ).
cnf(c128,plain,
( 'r6$upboole'(X1,X2,X2)
| ~ 'm1$upboole'(X2,X1)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[reflexivity_r6_pboole]) ).
cnf(c150,plain,
~ 'v1$uxboole$u0'(sK206),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c151,plain,
'm1$upboole'(sK207,sK206),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c152,plain,
'v2$urelat$u1'(sK207),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c153,plain,
'm1$upboole'(sK208,sK206),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c154,plain,
'v2$urelat$u1'(sK208),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c155,plain,
~ 'r6$upboole'(sK206,sK207,sK208),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c156,plain,
'k1$uclosure3'(sK206,sK208) = 'k1$uclosure3'(sK206,sK207),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c157,plain,
'k7$urelat$u1'(sK208,'k1$uclosure3'(sK206,sK208)) = 'k7$urelat$u1'(sK207,'k1$uclosure3'(sK206,sK207)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'r6$upboole'(sK206,X0,X0)
| ~ 'm1$upboole'(X0,sK206) ),
inference(resolution,[status(thm)],[c128,c151]) ).
cnf(d1,plain,
'r6$upboole'(sK206,sK207,sK207),
inference(resolution,[status(thm)],[d0,c151]) ).
cnf(d2,plain,
( ~ 'v2$urelat$u1'(sK207)
| 'v1$uxboole$u0'(sK206)
| 'k1$ufunct$u4'('k1$upboole'(sK206),'k7$urelat$u1'(sK207,'k1$uclosure3'(sK206,sK207))) = sK207 ),
inference(resolution,[status(thm)],[c151,c2]) ).
cnf(d3,plain,
( ~ 'v2$urelat$u1'(sK207)
| 'k1$ufunct$u4'('k1$upboole'(sK206),'k7$urelat$u1'(sK207,'k1$uclosure3'(sK206,sK207))) = sK207 ),
inference(resolution,[status(thm)],[c150,d2]) ).
cnf(d4,plain,
'k1$ufunct$u4'('k1$upboole'(sK206),'k7$urelat$u1'(sK207,'k1$uclosure3'(sK206,sK207))) = sK207,
inference(resolution,[status(thm)],[c152,d3]) ).
cnf(d5,plain,
'k7$urelat$u1'(sK208,'k1$uclosure3'(sK206,sK207)) = 'k7$urelat$u1'(sK207,'k1$uclosure3'(sK206,sK207)),
inference(demodulation,[status(thm)],[c157,c156]) ).
cnf(d6,plain,
( ~ 'v2$urelat$u1'(sK208)
| 'v1$uxboole$u0'(sK206)
| 'k1$ufunct$u4'('k1$upboole'(sK206),'k7$urelat$u1'(sK208,'k1$uclosure3'(sK206,sK208))) = sK208 ),
inference(resolution,[status(thm)],[c153,c2]) ).
cnf(d7,plain,
( ~ 'v2$urelat$u1'(sK208)
| 'v1$uxboole$u0'(sK206)
| 'k1$ufunct$u4'('k1$upboole'(sK206),'k7$urelat$u1'(sK208,'k1$uclosure3'(sK206,sK207))) = sK208 ),
inference(demodulation,[status(thm)],[d6,c156]) ).
cnf(d8,plain,
( ~ 'v2$urelat$u1'(sK208)
| 'v1$uxboole$u0'(sK206)
| 'k1$ufunct$u4'('k1$upboole'(sK206),'k7$urelat$u1'(sK207,'k1$uclosure3'(sK206,sK207))) = sK208 ),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ 'v2$urelat$u1'(sK208)
| 'v1$uxboole$u0'(sK206)
| sK207 = sK208 ),
inference(demodulation,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
( ~ 'v2$urelat$u1'(sK208)
| sK207 = sK208 ),
inference(resolution,[status(thm)],[c150,d9]) ).
cnf(d11,plain,
sK207 = sK208,
inference(resolution,[status(thm)],[c154,d10]) ).
cnf(d12,plain,
~ 'r6$upboole'(sK206,sK207,sK207),
inference(demodulation,[status(thm)],[c155,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG226+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 21:37:55 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.00/20.01 % SZS status Theorem for theBenchmark.p
% 16.00/20.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------