%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG226+3 : TPTP v9.3.1. Released v3.4.0.
% 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 06:48:10 AM UTC 2026
% Result : Theorem 22.13s 27.49s
% Output : CNFRefutation 22.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% 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 : 57 ( 20 ~; 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 : 18 ( 3 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$u0'(X0) ),
inference(clausification,[status(esa)],[t6_closure3]) ).
cnf(c145,plain,
( 'r6$upboole'(X1,X2,X2)
| ~ 'm1$upboole'(X2,X1)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[reflexivity_r6_pboole]) ).
cnf(c170,plain,
~ 'v1$uxboole$u0'(sK247),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c171,plain,
'm1$upboole'(sK248,sK247),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c172,plain,
'v2$urelat$u1'(sK248),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c173,plain,
'm1$upboole'(sK249,sK247),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c174,plain,
'v2$urelat$u1'(sK249),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c175,plain,
~ 'r6$upboole'(sK247,sK248,sK249),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c176,plain,
'k1$uclosure3'(sK247,sK249) = 'k1$uclosure3'(sK247,sK248),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c177,plain,
'k7$urelat$u1'(sK249,'k1$uclosure3'(sK247,sK249)) = 'k7$urelat$u1'(sK248,'k1$uclosure3'(sK247,sK248)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'r6$upboole'(sK247,sK248,sK248)
| ~ 'm1$upboole'(X0,sK247) ),
inference(resolution,[status(thm)],[c145,c171]) ).
cnf(d1,plain,
( ~ 'v2$urelat$u1'(sK248)
| 'v1$uxboole$u0'(sK247)
| 'k1$ufunct$u4'('k1$upboole'(sK247),'k7$urelat$u1'(sK248,'k1$uclosure3'(sK247,sK248))) = sK248 ),
inference(resolution,[status(thm)],[c171,c2]) ).
cnf(d2,plain,
( ~ 'v2$urelat$u1'(sK248)
| 'k1$ufunct$u4'('k1$upboole'(sK247),'k7$urelat$u1'(sK248,'k1$uclosure3'(sK247,sK248))) = sK248 ),
inference(resolution,[status(thm)],[c170,d1]) ).
cnf(d3,plain,
'k1$ufunct$u4'('k1$upboole'(sK247),'k7$urelat$u1'(sK248,'k1$uclosure3'(sK247,sK248))) = sK248,
inference(resolution,[status(thm)],[c172,d2]) ).
cnf(d4,plain,
'k7$urelat$u1'(sK249,'k1$uclosure3'(sK247,sK248)) = 'k7$urelat$u1'(sK248,'k1$uclosure3'(sK247,sK248)),
inference(demodulation,[status(thm)],[c177,c176]) ).
cnf(d5,plain,
( ~ 'v2$urelat$u1'(sK249)
| 'v1$uxboole$u0'(sK247)
| 'k1$ufunct$u4'('k1$upboole'(sK247),'k7$urelat$u1'(sK249,'k1$uclosure3'(sK247,sK249))) = sK249 ),
inference(resolution,[status(thm)],[c173,c2]) ).
cnf(d6,plain,
( ~ 'v2$urelat$u1'(sK249)
| 'v1$uxboole$u0'(sK247)
| 'k1$ufunct$u4'('k1$upboole'(sK247),'k7$urelat$u1'(sK249,'k1$uclosure3'(sK247,sK248))) = sK249 ),
inference(demodulation,[status(thm)],[d5,c176]) ).
cnf(d7,plain,
( ~ 'v2$urelat$u1'(sK249)
| 'v1$uxboole$u0'(sK247)
| 'k1$ufunct$u4'('k1$upboole'(sK247),'k7$urelat$u1'(sK248,'k1$uclosure3'(sK247,sK248))) = sK249 ),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( ~ 'v2$urelat$u1'(sK249)
| 'v1$uxboole$u0'(sK247)
| sK248 = sK249 ),
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( ~ 'v2$urelat$u1'(sK249)
| sK248 = sK249 ),
inference(resolution,[status(thm)],[c170,d8]) ).
cnf(d10,plain,
sK248 = sK249,
inference(resolution,[status(thm)],[c174,d9]) ).
cnf(d11,plain,
~ 'r6$upboole'(sK247,sK248,sK248),
inference(demodulation,[status(thm)],[c175,d10]) ).
cnf(d12,plain,
~ 'm1$upboole'(X0,sK247),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,c171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG226+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 21:37:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.13/27.49 % SZS status Theorem for theBenchmark.p
% 22.13/27.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------