%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET838-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:33:22 AM UTC 2026
% Result : Unsatisfiable 34.52s 11.69s
% Output : CNFRefutation 34.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of clauses : 37 ( 15 unt; 11 nHn; 25 RR)
% Number of literals : 61 ( 60 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'v$uf'('v$ug'('v$ux')) = 'v$ux' ).
cnf(cls_conjecture_1,negated_conjecture,
( 'v$uf'('v$ug'(X0)) != X0
| X0 = 'v$ux' ) ).
cnf(cls_conjecture_2,negated_conjecture,
( 'v$ug'('v$uf'(X0)) != X0
| 'v$ug'('v$uf'('v$uxa'(X0))) = 'v$uxa'(X0) ) ).
cnf(cls_conjecture_3,negated_conjecture,
( 'v$ug'('v$uf'(X0)) != X0
| 'v$uxa'(X0) != X0 ) ).
cnf(cls_Datatype_Onot__None__eq__iff1_0,axiom,
( X0 = 'c$uDatatype$uOoption$uOSome'('c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1),X1)
| X0 = 'c$uDatatype$uOoption$uONone' ) ).
cnf(cls_Datatype_Onot__Some__eq__iff1_0,axiom,
( X0 = 'c$uDatatype$uOoption$uOSome'('c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1),X1)
| X0 = 'c$uDatatype$uOoption$uONone' ) ).
cnf(cls_Datatype_Ooption_Odistinct__2__iff1_0,axiom,
'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uONone' ).
cnf(cls_Datatype_Ooption_Oinject__iff1_0,axiom,
( X0 = X2
| 'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uOSome'(X2,X1) ) ).
cnf(c0,plain,
'v$uf'('v$ug'('v$ux')) = 'v$ux',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
( 'v$uf'('v$ug'(X0)) != X0
| X0 = 'v$ux' ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
( 'v$ug'('v$uf'(X0)) != X0
| 'v$ug'('v$uf'('v$uxa'(X0))) = 'v$uxa'(X0) ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c3,plain,
( 'v$ug'('v$uf'(X0)) != X0
| 'v$uxa'(X0) != X0 ),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c6,plain,
( X0 = 'c$uDatatype$uOoption$uOSome'('c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1),X1)
| X0 = 'c$uDatatype$uOoption$uONone' ),
inference(clausification,[status(esa)],[cls_Datatype_Onot__None__eq__iff1_0]) ).
cnf(c7,plain,
( X0 = 'c$uDatatype$uOoption$uOSome'('c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1),X1)
| X0 = 'c$uDatatype$uOoption$uONone' ),
inference(clausification,[status(esa)],[cls_Datatype_Onot__Some__eq__iff1_0]) ).
cnf(c9,plain,
'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uONone',
inference(clausification,[status(esa)],[cls_Datatype_Ooption_Odistinct__2__iff1_0]) ).
cnf(c10,plain,
( X0 = X2
| 'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uOSome'(X2,X1) ),
inference(clausification,[status(esa)],[cls_Datatype_Ooption_Oinject__iff1_0]) ).
cnf(d0,plain,
( 'v$ug'('v$uf'('v$uxa'('v$ug'('v$ux')))) = 'v$uxa'('v$ug'('v$ux'))
| 'v$ug'('v$ux') != 'v$ug'('v$ux') ),
inference(superposition,[status(thm)],[c0,c2]) ).
cnf(d1,plain,
( X0 = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1) = X2
| X0 != 'c$uDatatype$uOoption$uOSome'(X2,X1) ),
inference(superposition,[status(thm)],[c6,c10]) ).
cnf(d2,plain,
( 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0
| 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone' ),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0,
inference(resolution,[status(thm)],[c9,d2]) ).
cnf(d4,plain,
( X0 = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1) = 'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1) ),
inference(superposition,[status(thm)],[c7,d3]) ).
cnf(d5,plain,
( X0 = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1) = X2
| X0 != 'c$uDatatype$uOoption$uOSome'(X2,X1) ),
inference(superposition,[status(thm)],[c7,c10]) ).
cnf(d6,plain,
( 'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0
| 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone' ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0,
inference(resolution,[status(thm)],[c9,d6]) ).
cnf(d8,plain,
( 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0 ),
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( X0 = X0
| 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone' ),
inference(demodulation,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
X0 = X0,
inference(resolution,[status(thm)],[c9,d9]) ).
cnf(d11,plain,
'v$ug'('v$uf'('v$uxa'('v$ug'('v$ux')))) = 'v$uxa'('v$ug'('v$ux')),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( 'v$uf'('v$uxa'('v$ug'('v$ux'))) = 'v$ux'
| 'v$uf'('v$uxa'('v$ug'('v$ux'))) != 'v$uf'('v$uxa'('v$ug'('v$ux'))) ),
inference(superposition,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
'v$uf'('v$uxa'('v$ug'('v$ux'))) = 'v$ux',
inference(resolution,[status(thm)],[d10,d12]) ).
cnf(d14,plain,
'v$ug'('v$ux') = 'v$uxa'('v$ug'('v$ux')),
inference(demodulation,[status(thm)],[d11,d13]) ).
cnf(d15,plain,
( 'v$uxa'('v$uxa'('v$ug'('v$ux'))) != 'v$uxa'('v$ug'('v$ux'))
| 'v$uxa'('v$ug'('v$ux')) != 'v$uxa'('v$ug'('v$ux')) ),
inference(superposition,[status(thm)],[d11,c3]) ).
cnf(d16,plain,
'v$uxa'('v$uxa'('v$ug'('v$ux'))) != 'v$uxa'('v$ug'('v$ux')),
inference(resolution,[status(thm)],[d10,d15]) ).
cnf(d17,plain,
'v$uxa'('v$ug'('v$ux')) != 'v$uxa'('v$ug'('v$ux')),
inference(demodulation,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
'v$ug'('v$ux') != 'v$uxa'('v$ug'('v$ux')),
inference(demodulation,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
'v$ug'('v$ux') != 'v$ug'('v$ux'),
inference(demodulation,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d10,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET838-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n013.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:19:36 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.52/11.69 % SZS status Unsatisfiable for theBenchmark.p
% 34.52/11.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------