%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:18:56 AM UTC 2026
% Result : Theorem 17.34s 2.57s
% Output : CNFRefutation 17.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 22 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 140 ( 69 ~; 59 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 92 ( 5 sgn 33 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ) ).
fof(axiom_2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,X1) ) ) ).
fof(axiom_5,axiom,
! [X0] : id(X0,X0) ).
fof(axiom_6,axiom,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ) ).
fof(axiom_7,axiom,
! [X0,X1,X2] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ) ).
fof(axiom_9,axiom,
! [X0,X1,X2,X3] :
( ( r2(X2,X3)
& r2(X0,X1) )
| ( ~ r2(X2,X3)
& ~ r2(X0,X1) )
| ~ id(X1,X3)
| ~ id(X0,X2) ) ).
fof(axiom_1a,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r3(X0,X1,X5)
& r2(X5,X2) )
& ? [X3] :
( ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) )
& id(X3,X2) ) ) ).
fof(axiom_3a,axiom,
! [X0,X1] :
( id(X0,X1)
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( ~ r2(X0,X3)
| ~ id(X3,X2) ) ) ) ).
fof(axiom_4a,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) ) ).
fof(axiom_7a,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( ~ r1(X2)
| ~ id(X2,X1) ) ) ).
fof(oneunidtwo,conjecture,
! [X0] :
( ! [X3] :
( ~ r2(X3,X0)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) )
| ! [X1] :
( ~ id(X1,X0)
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ! [X3] :
( ~ r2(X3,X0)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) )
| ! [X1] :
( ~ id(X1,X0)
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
inference(negate_conjecture,[status(cth)],[oneunidtwo]) ).
cnf(c0,plain,
( ~ r1(X0)
| id(X0,sK0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c3,plain,
( ~ id(X0,sK0)
| r1(X0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c4,plain,
( ~ r2(X1,X0)
| id(X0,sK3(X1)) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c7,plain,
( ~ id(X1,sK3(X0))
| r2(X0,X1) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c16,plain,
id(X0,X0),
inference(clausification,[status(esa)],[axiom_5]) ).
cnf(c17,plain,
( id(X1,X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_6]) ).
cnf(c18,plain,
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_7]) ).
cnf(c24,plain,
( r2(X1,X3)
| ~ r2(X0,X2)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_9]) ).
cnf(c36,plain,
r2(X0,sK41(X1,X0)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c45,plain,
( id(X2,X3)
| ~ r2(X3,X1)
| ~ r2(X2,X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_3a]) ).
cnf(c46,plain,
id(sK54(X0),X0),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c57,plain,
( ~ r2(X2,X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_7a]) ).
cnf(c58,plain,
r1(sK69),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
r2(sK69,sK68),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
id(sK68,sK67),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c62,plain,
r2(sK71,sK70),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c63,plain,
r2(sK70,sK67),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ r2(X0,X1)
| id(sK3(X0),X1) ),
inference(resolution,[status(thm)],[c17,c4]) ).
cnf(d1,plain,
id(sK67,sK68),
inference(resolution,[status(thm)],[c17,c60]) ).
cnf(d2,plain,
( ~ id(X0,sK67)
| id(X0,sK68) ),
inference(resolution,[status(thm)],[c18,d1]) ).
cnf(d3,plain,
( ~ r2(X0,sK67)
| id(sK3(X0),sK68) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( id(sK68,sK3(X0))
| ~ r2(X0,sK67) ),
inference(resolution,[status(thm)],[d3,c17]) ).
cnf(d5,plain,
( r2(X0,sK68)
| ~ r2(X0,sK67) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( r2(X0,X1)
| ~ id(sK68,X1)
| ~ id(sK69,X0) ),
inference(resolution,[status(thm)],[c24,c59]) ).
cnf(d7,plain,
( r2(X0,sK67)
| ~ id(sK69,X0) ),
inference(resolution,[status(thm)],[d6,c60]) ).
cnf(d8,plain,
( ~ r1(sK69)
| r2(sK0,sK67) ),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
r2(sK0,sK67),
inference(resolution,[status(thm)],[c58,d8]) ).
cnf(d10,plain,
r2(sK0,sK68),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( ~ id(X0,sK68)
| id(X0,sK67) ),
inference(resolution,[status(thm)],[c18,c60]) ).
cnf(d12,plain,
id(sK54(sK68),sK67),
inference(resolution,[status(thm)],[d11,c46]) ).
cnf(d13,plain,
( ~ id(X0,sK54(sK68))
| id(X0,sK67) ),
inference(resolution,[status(thm)],[d12,c18]) ).
cnf(d14,plain,
( ~ r2(X0,sK54(sK68))
| id(sK3(X0),sK67) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
id(sK67,sK54(sK68)),
inference(resolution,[status(thm)],[d12,c17]) ).
cnf(d16,plain,
( r2(X0,X1)
| ~ id(sK67,X1)
| ~ id(sK70,X0) ),
inference(resolution,[status(thm)],[c24,c63]) ).
cnf(d17,plain,
( r2(sK70,X0)
| ~ id(sK67,X0) ),
inference(resolution,[status(thm)],[d16,c16]) ).
cnf(d18,plain,
r2(sK70,sK54(sK68)),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
id(sK3(sK70),sK67),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
( ~ id(X0,sK3(sK70))
| id(X0,sK67) ),
inference(resolution,[status(thm)],[d19,c18]) ).
cnf(d21,plain,
( ~ r2(sK70,X0)
| id(X0,sK67) ),
inference(resolution,[status(thm)],[d20,c4]) ).
cnf(d22,plain,
id(sK41(X0,sK70),sK67),
inference(resolution,[status(thm)],[d21,c36]) ).
cnf(d23,plain,
id(sK41(X0,sK70),sK68),
inference(resolution,[status(thm)],[d22,d2]) ).
cnf(d24,plain,
( ~ r2(X1,X3)
| ~ id(sK41(X2,X0),X3)
| id(X0,X1) ),
inference(resolution,[status(thm)],[c45,c36]) ).
cnf(d25,plain,
( ~ r2(X0,sK68)
| id(sK70,X0) ),
inference(resolution,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
id(sK70,sK0),
inference(resolution,[status(thm)],[d25,d10]) ).
cnf(d27,plain,
r1(sK70),
inference(resolution,[status(thm)],[d26,c3]) ).
cnf(d28,plain,
( ~ id(X0,sK70)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c57,c62]) ).
cnf(d29,plain,
~ r1(sK70),
inference(resolution,[status(thm)],[d28,c16]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.29 % Computer : n012.cluster.edu
% 0.05/0.29 % Model : x86_64 x86_64
% 0.05/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.29 % Memory : 8046.5625MB
% 0.05/0.29 % OS : Linux 6.8.0-71-generic
% 0.05/0.29 % CPULimit : 300
% 0.05/0.29 % WCLimit : 300
% 0.05/0.29 % DateTime : Sat Sep 26 04:30:36 UTC 2026
% 0.05/0.29 % CPUTime :
% 0.05/0.29 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.34/2.57 % SZS status Theorem for theBenchmark.p
% 17.34/2.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------