%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG225+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 : n005.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 30.20s 14.65s
% Output : CNFRefutation 30.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 76 ( 18 unt; 0 def)
% Number of atoms : 216 ( 59 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 232 ( 92 ~; 101 |; 15 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 2 sgn 32 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d16_pboole,axiom,
! [X0,X1] :
( 'm1$upboole'(X1,X0)
=> ( 'v2$urelat$u1'(X1)
<=> ! [X2] :
~ ( 'v1$uxboole$u0'('k1$ufunct$u1'(X1,X2))
& 'r2$uhidden'(X2,X0) ) ) ) ).
fof(d3_closure3,axiom,
! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( 'm1$upboole'(X1,X0)
=> ! [X2] :
( X2 = 'k1$uclosure3'(X0,X1)
<=> X2 = 'a$u2$u0$uclosure3'(X0,X1) ) ) ) ).
fof(d3_pboole,axiom,
! [X0,X1] :
( ( 'v1$ufunct$u1'(X1)
& 'v1$urelat$u1'(X1) )
=> ( 'm1$upboole'(X1,X0)
<=> 'k1$urelat$u1'(X1) = X0 ) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( 'r1$utarski'(X0,X1)
<=> ! [X2] :
( 'r2$uhidden'(X2,X0)
=> 'r2$uhidden'(X2,X1) ) ) ).
fof(dt_k1_funct_4,axiom,
! [X0,X1] :
( ( 'v1$ufunct$u1'(X1)
& 'v1$urelat$u1'(X1)
& 'v1$ufunct$u1'(X0)
& 'v1$urelat$u1'(X0) )
=> ( 'v1$ufunct$u1'('k1$ufunct$u4'(X0,X1))
& 'v1$urelat$u1'('k1$ufunct$u4'(X0,X1)) ) ) ).
fof(dt_k1_pboole,axiom,
! [X0] : 'm1$upboole'('k1$upboole'(X0),X0) ).
fof(dt_m1_pboole,axiom,
! [X0,X1] :
( 'm1$upboole'(X1,X0)
=> ( 'v1$ufunct$u1'(X1)
& 'v1$urelat$u1'(X1) ) ) ).
fof(fc1_xboole_0,axiom,
'v1$uxboole$u0'('k1$uxboole$u0') ).
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$u1'(X3,X1) ) ) ) ).
fof(idempotence_k1_funct_4,axiom,
! [X0,X1] :
( ( 'v1$ufunct$u1'(X1)
& 'v1$urelat$u1'(X1)
& 'v1$ufunct$u1'(X0)
& 'v1$urelat$u1'(X0) )
=> 'k1$ufunct$u4'(X0,X0) = X0 ) ).
fof(t1_closure3,axiom,
! [X0] :
( ~ 'v1$uxboole$u0'(X0)
=> ! [X1] :
( 'm1$upboole'(X1,X0)
=> ! [X2] :
( 'm1$upboole'(X2,X0)
=> 'k1$ufunct$u4'(X1,X2) = X2 ) ) ) ).
fof(t1_subset,axiom,
! [X0,X1] :
( 'r2$uhidden'(X0,X1)
=> 'm1$usubset$u1'(X0,X1) ) ).
fof(t97_relat_1,axiom,
! [X0,X1] :
( 'v1$urelat$u1'(X1)
=> ( 'r1$utarski'('k1$urelat$u1'(X1),X0)
=> 'k7$urelat$u1'(X1,X0) = X1 ) ) ).
fof(t6_closure3,conjecture,
! [X0] :
( ~ 'v1$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(negated_conjecture,negated_conjecture,
~ ! [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$uclosure3'(X0,X1))) ) ),
inference(negate_conjecture,[status(cth)],[t6_closure3]) ).
cnf(c14,plain,
( ~ 'v1$uxboole$u0'('k1$ufunct$u1'(X0,X2))
| ~ 'r2$uhidden'(X2,X1)
| ~ 'v2$urelat$u1'(X0)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[d16_pboole]) ).
cnf(c17,plain,
( 'a$u2$u0$uclosure3'(X0,X1) = X2
| 'k1$uclosure3'(X0,X1) != X2
| ~ 'm1$upboole'(X1,X0)
| 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[d3_closure3]) ).
cnf(c19,plain,
( 'k1$urelat$u1'(X0) = X1
| ~ 'm1$upboole'(X0,X1)
| ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X0) ),
inference(clausification,[status(esa)],[d3_pboole]) ).
cnf(c22,plain,
( 'r2$uhidden'(sK28(X0,X1),X0)
| 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c23,plain,
( ~ 'r2$uhidden'(sK28(X0,X1),X1)
| 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c25,plain,
( 'v1$urelat$u1'('k1$ufunct$u4'(X1,X0))
| ~ 'v1$urelat$u1'(X1)
| ~ 'v1$ufunct$u1'(X1)
| ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X0) ),
inference(clausification,[status(esa)],[dt_k1_funct_4]) ).
cnf(c27,plain,
'm1$upboole'('k1$upboole'(X0),X0),
inference(clausification,[status(esa)],[dt_k1_pboole]) ).
cnf(c29,plain,
( 'v1$urelat$u1'(X0)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_pboole]) ).
cnf(c30,plain,
( 'v1$ufunct$u1'(X0)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[dt_m1_pboole]) ).
cnf(c38,plain,
'v1$uxboole$u0'('k1$uxboole$u0'),
inference(clausification,[status(esa)],[fc1_xboole_0]) ).
cnf(c48,plain,
( ~ 'm1$upboole'(X3,X0)
| ~ 'm1$usubset$u1'(X1,X0)
| 'k1$ufunct$u1'(X3,X1) = 'k1$uxboole$u0'
| 'r2$uhidden'(X2,'a$u2$u0$uclosure3'(X0,X3))
| X1 != X2
| 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[fraenkel_a_2_0_closure3]) ).
cnf(c53,plain,
( ~ 'v1$ufunct$u1'(X1)
| ~ 'v1$urelat$u1'(X1)
| ~ 'v1$ufunct$u1'(X0)
| 'k1$ufunct$u4'(X0,X0) = X0
| ~ 'v1$urelat$u1'(X0) ),
inference(clausification,[status(esa)],[idempotence_k1_funct_4]) ).
cnf(c100,plain,
( 'k1$ufunct$u4'(X1,X2) = X2
| ~ 'm1$upboole'(X2,X0)
| ~ 'm1$upboole'(X1,X0)
| 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[t1_closure3]) ).
cnf(c101,plain,
( 'm1$usubset$u1'(X0,X1)
| ~ 'r2$uhidden'(X0,X1) ),
inference(clausification,[status(esa)],[t1_subset]) ).
cnf(c114,plain,
( ~ 'r1$utarski'('k1$urelat$u1'(X0),X1)
| 'k7$urelat$u1'(X0,X1) = X0
| ~ 'v1$urelat$u1'(X0) ),
inference(clausification,[status(esa)],[t97_relat_1]) ).
cnf(c115,plain,
~ 'v1$uxboole$u0'(sK110),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c116,plain,
'm1$upboole'(sK111,sK110),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c117,plain,
'v2$urelat$u1'(sK111),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c118,plain,
'k1$ufunct$u4'('k1$upboole'(sK110),'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111))) != sK111,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'm1$upboole'(X0,sK110)
| 'v1$uxboole$u0'(sK110)
| 'k1$ufunct$u4'(X0,sK111) = sK111 ),
inference(resolution,[status(thm)],[c100,c116]) ).
cnf(d1,plain,
( ~ 'm1$upboole'(X0,sK110)
| 'k1$ufunct$u4'(X0,sK111) = sK111 ),
inference(resolution,[status(thm)],[c115,d0]) ).
cnf(d2,plain,
'k1$ufunct$u4'('k1$upboole'(sK110),sK111) = sK111,
inference(resolution,[status(thm)],[d1,c27]) ).
cnf(d3,plain,
( ~ 'v1$urelat$u1'(sK111)
| ~ 'v1$ufunct$u1'(sK111)
| 'k1$urelat$u1'(sK111) = sK110 ),
inference(resolution,[status(thm)],[c19,c116]) ).
cnf(d4,plain,
'v1$urelat$u1'(sK111),
inference(resolution,[status(thm)],[c29,c116]) ).
cnf(d5,plain,
( ~ 'v1$ufunct$u1'(sK111)
| 'k1$urelat$u1'(sK111) = sK110 ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'v1$ufunct$u1'(sK111),
inference(resolution,[status(thm)],[c30,c116]) ).
cnf(d7,plain,
'k1$urelat$u1'(sK111) = sK110,
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ 'v1$urelat$u1'(sK111)
| 'k7$urelat$u1'(sK111,X0) = sK111
| ~ 'r1$utarski'(sK110,X0) ),
inference(superposition,[status(thm)],[d7,c114]) ).
cnf(d9,plain,
( ~ 'r1$utarski'(sK110,X0)
| 'k7$urelat$u1'(sK111,X0) = sK111 ),
inference(resolution,[status(thm)],[d4,d8]) ).
cnf(d10,plain,
( 'r1$utarski'(X0,X1)
| 'm1$usubset$u1'(sK28(X0,X1),X0) ),
inference(resolution,[status(thm)],[c101,c22]) ).
cnf(d11,plain,
( ~ 'm1$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)],[c48]) ).
cnf(d12,plain,
( ~ 'm1$upboole'(X1,X0)
| 'v1$uxboole$u0'(X0)
| 'a$u2$u0$uclosure3'(X0,X1) = 'k1$uclosure3'(X0,X1) ),
inference(equality_resolution,[status(thm)],[c17]) ).
cnf(d13,plain,
( 'v1$uxboole$u0'(sK110)
| 'a$u2$u0$uclosure3'(sK110,sK111) = 'k1$uclosure3'(sK110,sK111) ),
inference(resolution,[status(thm)],[d12,c116]) ).
cnf(d14,plain,
'a$u2$u0$uclosure3'(sK110,sK111) = 'k1$uclosure3'(sK110,sK111),
inference(resolution,[status(thm)],[c115,d13]) ).
cnf(d15,plain,
( ~ 'm1$usubset$u1'(X0,sK110)
| ~ 'm1$upboole'(sK111,sK110)
| 'v1$uxboole$u0'(sK110)
| 'k1$ufunct$u1'(sK111,X0) = 'k1$uxboole$u0'
| 'r2$uhidden'(X0,'k1$uclosure3'(sK110,sK111)) ),
inference(superposition,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( ~ 'm1$usubset$u1'(X0,sK110)
| ~ 'm1$upboole'(sK111,sK110)
| 'r2$uhidden'(X0,'k1$uclosure3'(sK110,sK111))
| 'k1$ufunct$u1'(sK111,X0) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[c115,d15]) ).
cnf(d17,plain,
( ~ 'm1$usubset$u1'(X0,sK110)
| 'r2$uhidden'(X0,'k1$uclosure3'(sK110,sK111))
| 'k1$ufunct$u1'(sK111,X0) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[c116,d16]) ).
cnf(d18,plain,
( 'r1$utarski'(X0,'k1$uclosure3'(sK110,sK111))
| ~ 'm1$usubset$u1'(sK28(X0,'k1$uclosure3'(sK110,sK111)),sK110)
| 'k1$ufunct$u1'(sK111,sK28(X0,'k1$uclosure3'(sK110,sK111))) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[d17,c23]) ).
cnf(d19,plain,
( 'r1$utarski'(sK110,'k1$uclosure3'(sK110,sK111))
| 'r1$utarski'(sK110,'k1$uclosure3'(sK110,sK111))
| 'k1$ufunct$u1'(sK111,sK28(sK110,'k1$uclosure3'(sK110,sK111))) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
( 'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111)) = sK111
| 'k1$ufunct$u1'(sK111,sK28(sK110,'k1$uclosure3'(sK110,sK111))) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[d19,d9]) ).
cnf(d21,plain,
( 'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111)) = sK111
| ~ 'v2$urelat$u1'(sK111)
| ~ 'm1$upboole'(sK111,X0)
| ~ 'r2$uhidden'(sK28(sK110,'k1$uclosure3'(sK110,sK111)),X0)
| ~ 'v1$uxboole$u0'('k1$uxboole$u0') ),
inference(superposition,[status(thm)],[d20,c14]) ).
cnf(d22,plain,
( ~ 'm1$upboole'(sK111,X0)
| ~ 'v1$uxboole$u0'('k1$uxboole$u0')
| ~ 'r2$uhidden'(sK28(sK110,'k1$uclosure3'(sK110,sK111)),X0)
| 'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111)) = sK111 ),
inference(resolution,[status(thm)],[c117,d21]) ).
cnf(d23,plain,
( ~ 'm1$upboole'(sK111,X0)
| ~ 'r2$uhidden'(sK28(sK110,'k1$uclosure3'(sK110,sK111)),X0)
| 'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111)) = sK111 ),
inference(resolution,[status(thm)],[c38,d22]) ).
cnf(d24,plain,
( 'r1$utarski'(sK110,'k1$uclosure3'(sK110,sK111))
| ~ 'm1$upboole'(sK111,sK110)
| 'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111)) = sK111 ),
inference(resolution,[status(thm)],[d23,c22]) ).
cnf(d25,plain,
( 'r1$utarski'(sK110,'k1$uclosure3'(sK110,sK111))
| 'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111)) = sK111 ),
inference(resolution,[status(thm)],[c116,d24]) ).
cnf(d26,plain,
( 'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111)) = sK111
| 'k7$urelat$u1'(sK111,'k1$uclosure3'(sK110,sK111)) = sK111 ),
inference(resolution,[status(thm)],[d25,d9]) ).
cnf(d27,plain,
'k1$ufunct$u4'('k1$upboole'(sK110),sK111) != sK111,
inference(demodulation,[status(thm)],[c118,d26]) ).
cnf(d28,plain,
sK111 != sK111,
inference(demodulation,[status(thm)],[d27,d2]) ).
cnf(d29,plain,
( ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(sK111)
| ~ 'v1$ufunct$u1'(X0)
| 'k1$ufunct$u4'(X0,X0) = X0 ),
inference(resolution,[status(thm)],[c53,d4]) ).
cnf(d30,plain,
( ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X0)
| 'k1$ufunct$u4'(X0,X0) = X0 ),
inference(resolution,[status(thm)],[d6,d29]) ).
cnf(d31,plain,
( ~ 'v1$ufunct$u1'(sK111)
| 'k1$ufunct$u4'(sK111,sK111) = sK111 ),
inference(resolution,[status(thm)],[d30,d4]) ).
cnf(d32,plain,
'k1$ufunct$u4'(sK111,sK111) = sK111,
inference(resolution,[status(thm)],[d6,d31]) ).
cnf(d33,plain,
( ~ 'v1$urelat$u1'(X1)
| ~ 'v1$urelat$u1'(X0)
| ~ 'v1$ufunct$u1'(X1)
| ~ 'v1$ufunct$u1'(X0)
| ~ 'v1$ufunct$u1'('k1$ufunct$u4'(X0,X1))
| 'k1$ufunct$u4'('k1$ufunct$u4'(X0,X1),'k1$ufunct$u4'(X0,X1)) = 'k1$ufunct$u4'(X0,X1) ),
inference(resolution,[status(thm)],[d30,c25]) ).
cnf(d34,plain,
( ~ 'v1$urelat$u1'(sK111)
| ~ 'v1$urelat$u1'(sK111)
| ~ 'v1$ufunct$u1'(sK111)
| ~ 'v1$ufunct$u1'(sK111)
| 'k1$ufunct$u4'('k1$ufunct$u4'(sK111,sK111),'k1$ufunct$u4'(sK111,sK111)) = 'k1$ufunct$u4'(sK111,sK111)
| ~ 'v1$ufunct$u1'(sK111) ),
inference(superposition,[status(thm)],[d32,d33]) ).
cnf(d35,plain,
( ~ 'v1$urelat$u1'(sK111)
| ~ 'v1$ufunct$u1'(sK111)
| 'k1$ufunct$u4'(sK111,'k1$ufunct$u4'(sK111,sK111)) = 'k1$ufunct$u4'(sK111,sK111) ),
inference(demodulation,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
( ~ 'v1$urelat$u1'(sK111)
| ~ 'v1$ufunct$u1'(sK111)
| 'k1$ufunct$u4'(sK111,sK111) = 'k1$ufunct$u4'(sK111,sK111) ),
inference(demodulation,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
( ~ 'v1$urelat$u1'(sK111)
| ~ 'v1$ufunct$u1'(sK111)
| sK111 = 'k1$ufunct$u4'(sK111,sK111) ),
inference(demodulation,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
( ~ 'v1$urelat$u1'(sK111)
| ~ 'v1$ufunct$u1'(sK111)
| sK111 = sK111 ),
inference(demodulation,[status(thm)],[d37,d32]) ).
cnf(d39,plain,
( ~ 'v1$ufunct$u1'(sK111)
| sK111 = sK111 ),
inference(resolution,[status(thm)],[d4,d38]) ).
cnf(d40,plain,
sK111 = sK111,
inference(resolution,[status(thm)],[d6,d39]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[d40,d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG225+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
% 0.09/10.39 % Computer : n005.cluster.edu
% 0.09/10.39 % Model : x86_64 x86_64
% 0.09/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.39 % Memory : 8046.5625MB
% 0.09/10.39 % OS : Linux 6.8.0-71-generic
% 0.09/10.39 % CPULimit : 300
% 0.09/10.39 % WCLimit : 300
% 0.09/10.39 % DateTime : Sat Sep 26 21:34:58 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.20/14.65 % SZS status Theorem for theBenchmark.p
% 30.20/14.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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