%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG227+1 : 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 : n026.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 11.15s 1.97s
% Output : CNFRefutation 11.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 58 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 21 |; 3 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_closure3,axiom,
! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( 'm1$upboole'(X1,X0)
=> ! [X2] :
( X2 = 'k1$uclosure3'(X0,X1)
<=> X2 = 'a$u2$u0$uclosure3'(X0,X1) ) ) ) ).
fof(fraenkel_a_2_0_closure3,axiom,
! [X0,X1,X2] :
( ( 'm1$upboole'(X2,X1)
& ~ 'v1$uxboole$u0'(X1) )
=> ( 'r2$uhidden'(X0,'a$u2$u0$uclosure3'(X1,X2))
<=> ? [X3] :
( 'k1$ufunct$u1'(X2,X3) != 'k1$uxboole$u0'
& X0 = X3
& 'm1$usubset$u1'(X3,X1) ) ) ) ).
fof(t8_closure3,conjecture,
! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( 'm1$upboole'(X1,X0)
=> ! [X2] :
( 'm1$usubset$u1'(X2,X0)
=> ( ~ 'r2$uhidden'(X2,'k1$uclosure3'(X0,X1))
=> 'k1$ufunct$u1'(X1,X2) = 'k1$uxboole$u0' ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( 'm1$upboole'(X1,X0)
=> ! [X2] :
( 'm1$usubset$u1'(X2,X0)
=> ( ~ 'r2$uhidden'(X2,'k1$uclosure3'(X0,X1))
=> 'k1$ufunct$u1'(X1,X2) = 'k1$uxboole$u0' ) ) ) ),
inference(negate_conjecture,[status(cth)],[t8_closure3]) ).
cnf(c7,plain,
( X2 = 'a$u2$u0$uclosure3'(X0,X1)
| X2 != 'k1$uclosure3'(X0,X1)
| ~ 'm1$upboole'(X1,X0)
| 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[d3_closure3]) ).
cnf(c17,plain,
( 'v1$uxboole$u0'(X1)
| 'r2$uhidden'(X3,'a$u2$u0$uclosure3'(X1,X0))
| 'k1$ufunct$u1'(X0,X2) = 'k1$uxboole$u0'
| X3 != X2
| ~ 'm1$usubset$u1'(X2,X1)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[fraenkel_a_2_0_closure3]) ).
cnf(c45,plain,
~ 'v1$uxboole$u0'(sK39),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c46,plain,
'm1$upboole'(sK40,sK39),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
'm1$usubset$u1'(sK41,sK39),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
~ 'r2$uhidden'(sK41,'k1$uclosure3'(sK39,sK40)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
'k1$ufunct$u1'(sK40,sK41) != 'k1$uxboole$u0',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'm1$upboole'(X1,X0)
| 'v1$uxboole$u0'(X0)
| 'k1$uclosure3'(X0,X1) = 'a$u2$u0$uclosure3'(X0,X1) ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d1,plain,
( 'v1$uxboole$u0'(sK39)
| 'k1$uclosure3'(sK39,sK40) = 'a$u2$u0$uclosure3'(sK39,sK40) ),
inference(resolution,[status(thm)],[d0,c46]) ).
cnf(d2,plain,
'k1$uclosure3'(sK39,sK40) = 'a$u2$u0$uclosure3'(sK39,sK40),
inference(resolution,[status(thm)],[c45,d1]) ).
cnf(d3,plain,
~ 'r2$uhidden'(sK41,'a$u2$u0$uclosure3'(sK39,sK40)),
inference(demodulation,[status(thm)],[c48,d2]) ).
cnf(d4,plain,
( ~ 'm1$usubset$u1'(X1,X2)
| ~ 'm1$upboole'(X0,X2)
| 'v1$uxboole$u0'(X2)
| 'r2$uhidden'(X1,'a$u2$u0$uclosure3'(X2,X0))
| 'k1$ufunct$u1'(X0,X1) = 'k1$uxboole$u0' ),
inference(equality_resolution,[status(thm)],[c17]) ).
cnf(d5,plain,
( ~ 'm1$usubset$u1'(sK41,sK39)
| ~ 'm1$upboole'(sK40,sK39)
| 'v1$uxboole$u0'(sK39)
| 'k1$ufunct$u1'(sK40,sK41) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ 'm1$usubset$u1'(sK41,sK39)
| ~ 'm1$upboole'(sK40,sK39)
| 'k1$ufunct$u1'(sK40,sK41) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[c45,d5]) ).
cnf(d7,plain,
( ~ 'm1$usubset$u1'(sK41,sK39)
| 'k1$ufunct$u1'(sK40,sK41) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[c46,d6]) ).
cnf(d8,plain,
'k1$ufunct$u1'(sK40,sK41) = 'k1$uxboole$u0',
inference(resolution,[status(thm)],[c47,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c49,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 21:39:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.15/1.97 % SZS status Theorem for theBenchmark.p
% 11.15/1.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------