%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% 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 09:21:51 AM UTC 2026
% Result : Theorem 9.73s 1.64s
% Output : CNFRefutation 9.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 2 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 56 ( 21 ~; 21 |; 0 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 34 ( 2 sgn 2 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_6,conjecture,
? [X0,X1] :
! [X2] :
( ( 'big$uf'(X0,X1)
=> ( 'big$uf'(X0,X2)
<=> 'big$ug'(X1,X2) ) )
=> ( ( 'big$uf'(X0,X1)
<=> ( 'big$uf'(X2,X2)
=> 'big$ug'(X2,X2) ) )
=> ( 'big$ug'(X0,X1)
<=> 'big$ug'(X2,X2) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] :
! [X2] :
( ( 'big$uf'(X0,X1)
=> ( 'big$uf'(X0,X2)
<=> 'big$ug'(X1,X2) ) )
=> ( ( 'big$uf'(X0,X1)
<=> ( 'big$uf'(X2,X2)
=> 'big$ug'(X2,X2) ) )
=> ( 'big$ug'(X0,X1)
<=> 'big$ug'(X2,X2) ) ) ),
inference(negate_conjecture,[status(cth)],[church_46_14_6]) ).
cnf(c0,plain,
( 'big$ug'(X1,sK2(X0,X1))
| ~ 'big$uf'(X0,sK2(X0,X1))
| ~ 'big$uf'(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1,plain,
( ~ 'big$ug'(X1,sK2(X0,X1))
| 'big$uf'(X0,sK2(X0,X1))
| ~ 'big$uf'(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c2,plain,
( 'big$ug'(sK2(X0,X1),sK2(X0,X1))
| ~ 'big$uf'(sK2(X0,X1),sK2(X0,X1))
| ~ 'big$uf'(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c3,plain,
( 'big$uf'(sK2(X0,X1),sK2(X0,X1))
| 'big$uf'(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
( ~ 'big$ug'(sK2(X0,X1),sK2(X0,X1))
| 'big$uf'(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c6,plain,
( 'big$ug'(sK2(X0,X1),sK2(X0,X1))
| 'big$ug'(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
( ~ 'big$ug'(X0,X1)
| ~ 'big$ug'(sK2(X0,X1),sK2(X0,X1)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'big$uf'(X0,X1)
| 'big$ug'(X0,X1) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d1,plain,
( 'big$ug'(X1,sK2(X0,X1))
| ~ 'big$uf'(X0,X1)
| 'big$ug'(X0,sK2(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( 'big$ug'(X0,sK2(X0,X0))
| ~ 'big$uf'(X0,X0) ),
inference(factoring,[status(thm)],[d1]) ).
cnf(d3,plain,
( 'big$uf'(X0,sK2(X0,X0))
| ~ 'big$uf'(X0,X0)
| ~ 'big$uf'(X0,X0) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( 'big$ug'(sK2(X0,X1),sK2(X0,X1))
| ~ 'big$uf'(X0,X1)
| 'big$ug'(sK2(X0,X1),sK2(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d5,plain,
( ~ 'big$ug'(X0,X1)
| ~ 'big$uf'(X0,X1) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( ~ 'big$uf'(X0,sK2(X0,X0))
| ~ 'big$uf'(X0,X0) ),
inference(resolution,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
( ~ 'big$uf'(X0,X0)
| ~ 'big$uf'(X0,X0) ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
'big$uf'(X0,X1),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 17:35:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.73/1.64 % SZS status Theorem for theBenchmark.p
% 9.73/1.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------