%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN328+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 09:21:50 AM UTC 2026
% Result : Theorem 9.77s 1.78s
% Output : CNFRefutation 9.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 63 ( 15 ~; 24 |; 4 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 25 ( 3 sgn 4 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_12_3,conjecture,
? [X0] :
! [X1,X2] :
( ( ( 'big$uf'(X1)
=> 'big$ug'(X1) )
<=> 'big$uf'(X0) )
=> ( ( ( 'big$uf'(X1)
=> 'big$uh'(X1) )
<=> 'big$ug'(X0) )
=> ( ( ( ( 'big$uf'(X1)
=> 'big$ug'(X1) )
=> 'big$uh'(X1) )
<=> 'big$uh'(X0) )
=> ( 'big$uh'(X2)
& 'big$ug'(X2)
& 'big$uf'(X2) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
! [X1,X2] :
( ( ( 'big$uf'(X1)
=> 'big$ug'(X1) )
<=> 'big$uf'(X0) )
=> ( ( ( 'big$uf'(X1)
=> 'big$uh'(X1) )
<=> 'big$ug'(X0) )
=> ( ( ( ( 'big$uf'(X1)
=> 'big$ug'(X1) )
=> 'big$uh'(X1) )
<=> 'big$uh'(X0) )
=> ( 'big$uh'(X2)
& 'big$ug'(X2)
& 'big$uf'(X2) ) ) ) ),
inference(negate_conjecture,[status(cth)],[church_46_12_3]) ).
cnf(c0,plain,
( 'big$uf'(X0)
| 'big$uf'(sK1(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1,plain,
( 'big$uf'(X0)
| ~ 'big$ug'(sK1(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
( 'big$ug'(X0)
| ~ 'big$uh'(sK1(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c5,plain,
( ~ 'big$ug'(X0)
| 'big$uh'(sK1(X0))
| ~ 'big$uf'(sK1(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c6,plain,
( 'big$uh'(X0)
| 'big$ug'(sK1(X0))
| ~ 'big$uf'(sK1(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
( 'big$uh'(X0)
| ~ 'big$uh'(sK1(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
( ~ 'big$uh'(sK2(X0))
| ~ 'big$ug'(sK2(X0))
| ~ 'big$uf'(sK2(X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'big$uf'(X0)
| 'big$uh'(X0)
| 'big$ug'(sK1(X0)) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d1,plain,
( 'big$uf'(X0)
| 'big$uh'(X0)
| 'big$uf'(X0) ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( 'big$uh'(X0)
| 'big$uf'(sK1(X0)) ),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( 'big$uh'(X0)
| 'big$ug'(sK1(X0))
| 'big$uh'(X0) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( 'big$uh'(sK1(X0))
| ~ 'big$ug'(X0)
| 'big$uh'(X0) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d5,plain,
( 'big$uh'(X0)
| 'big$uh'(X0)
| ~ 'big$ug'(X0) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( 'big$uh'(X0)
| 'big$uh'(sK1(X0)) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( 'big$uh'(X0)
| 'big$uh'(X0) ),
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
( ~ 'big$ug'(sK2(X0))
| ~ 'big$uf'(sK2(X0)) ),
inference(resolution,[status(thm)],[d7,c10]) ).
cnf(d9,plain,
'big$ug'(X0),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d10,plain,
~ 'big$uf'(sK2(X0)),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
'big$uf'(X0),
inference(resolution,[status(thm)],[d9,c1]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN328+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.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 17:40:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.77/1.78 % SZS status Theorem for theBenchmark.p
% 9.77/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------