%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN353+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 : n003.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 09:21:55 AM UTC 2026
% Result : Theorem 10.71s 1.92s
% Output : CNFRefutation 10.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 1
% Syntax : Number of formulae : 53 ( 3 unt; 0 def)
% Number of atoms : 202 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 212 ( 63 ~; 113 |; 8 &)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 110 ( 4 sgn 4 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_5,conjecture,
! [X0] :
? [X1,X2,X3] :
! [X4] :
( ( 'big$uf'(X1,X2,X3)
=> ( 'big$uf'(X0,X0,X4)
=> ( 'big$uf'(X3,X1,X2)
| 'big$uf'(X2,X3,X1) ) ) )
=> ( ( ( 'big$uf'(X3,X1,X2)
=> ( 'big$uf'(X2,X3,X1)
& 'big$uf'(X1,X2,X3) ) )
<=> 'big$uf'(X2,X1,X4) )
=> ( ( ( 'big$uf'(X2,X3,X1)
=> ( 'big$uf'(X3,X1,X2)
& 'big$uf'(X1,X2,X3) ) )
<=> 'big$uf'(X1,X4,X2) )
=> ( ( ( ( 'big$uf'(X3,X1,X2)
=> ~ 'big$uf'(X2,X3,X1) )
=> 'big$uf'(X1,X2,X3) )
<=> 'big$uf'(X4,X2,X1) )
=> ( ( 'big$uf'(X3,X1,X2)
& 'big$uf'(X2,X3,X1)
& 'big$uf'(X1,X2,X3) )
<=> 'big$uf'(X4,X4,X4) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
? [X1,X2,X3] :
! [X4] :
( ( 'big$uf'(X1,X2,X3)
=> ( 'big$uf'(X0,X0,X4)
=> ( 'big$uf'(X3,X1,X2)
| 'big$uf'(X2,X3,X1) ) ) )
=> ( ( ( 'big$uf'(X3,X1,X2)
=> ( 'big$uf'(X2,X3,X1)
& 'big$uf'(X1,X2,X3) ) )
<=> 'big$uf'(X2,X1,X4) )
=> ( ( ( 'big$uf'(X2,X3,X1)
=> ( 'big$uf'(X3,X1,X2)
& 'big$uf'(X1,X2,X3) ) )
<=> 'big$uf'(X1,X4,X2) )
=> ( ( ( ( 'big$uf'(X3,X1,X2)
=> ~ 'big$uf'(X2,X3,X1) )
=> 'big$uf'(X1,X2,X3) )
<=> 'big$uf'(X4,X2,X1) )
=> ( ( 'big$uf'(X3,X1,X2)
& 'big$uf'(X2,X3,X1)
& 'big$uf'(X1,X2,X3) )
<=> 'big$uf'(X4,X4,X4) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[church_46_18_5]) ).
cnf(c0,plain,
( 'big$uf'(X2,X0,X1)
| 'big$uf'(X1,X2,X0)
| ~ 'big$uf'(sK0,sK0,sK4(X0,X1,X2))
| ~ 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1,plain,
( 'big$uf'(X2,X1,sK4(X1,X2,X0))
| 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c3,plain,
( ~ 'big$uf'(X2,X1,sK4(X1,X2,X0))
| 'big$uf'(X1,X2,X0)
| ~ 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
( ~ 'big$uf'(X2,X1,sK4(X1,X2,X0))
| 'big$uf'(X2,X0,X1)
| ~ 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c5,plain,
( 'big$uf'(X2,sK4(X2,X0,X1),X0)
| 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
( ~ 'big$uf'(X2,sK4(X2,X0,X1),X0)
| 'big$uf'(X2,X0,X1)
| ~ 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
( ~ 'big$uf'(X2,sK4(X2,X0,X1),X0)
| 'big$uf'(X1,X2,X0)
| ~ 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
( 'big$uf'(sK4(X1,X2,X0),X2,X1)
| ~ 'big$uf'(X2,X0,X1)
| ~ 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11,plain,
( ~ 'big$uf'(sK4(X1,X2,X0),X2,X1)
| 'big$uf'(X1,X2,X0)
| 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
( ~ 'big$uf'(sK4(X2,X0,X1),X0,X2)
| 'big$uf'(X2,X0,X1)
| 'big$uf'(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
( ~ 'big$uf'(X2,X0,X1)
| ~ 'big$uf'(X1,X2,X0)
| ~ 'big$uf'(X0,X1,X2)
| ~ 'big$uf'(sK4(X0,X1,X2),sK4(X0,X1,X2),sK4(X0,X1,X2)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'big$uf'(sK0,sK0,X0)
| 'big$uf'(sK0,X0,sK0)
| 'big$uf'(X0,sK0,sK0)
| 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,sK4(sK0,sK0,X0),sK0)
| 'big$uf'(sK4(sK0,sK0,X0),sK0,sK0) ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( 'big$uf'(sK0,sK0,X0)
| 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,sK4(sK0,sK0,X0),sK0)
| 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d3,plain,
( ~ 'big$uf'(sK0,X0,sK0)
| 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,sK0,X0)
| 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| 'big$uf'(sK4(sK0,sK0,X0),sK0,sK0) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
( 'big$uf'(sK0,sK0,X0)
| 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| 'big$uf'(sK0,X0,sK0) ),
inference(resolution,[status(thm)],[d4,c12]) ).
cnf(d6,plain,
( ~ 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,sK0,X0)
| 'big$uf'(sK0,X0,sK0) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( ~ 'big$uf'(X0,sK0,sK0)
| ~ 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| 'big$uf'(sK0,sK4(sK0,sK0,X0),sK0) ),
inference(resolution,[status(thm)],[d6,c9]) ).
cnf(d8,plain,
( 'big$uf'(sK0,sK0,X0)
| ~ 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| ~ 'big$uf'(sK0,X0,sK0)
| ~ 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
( ~ 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,sK0,X0)
| 'big$uf'(sK0,sK0,X0)
| ~ 'big$uf'(sK0,X0,sK0)
| ~ 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| ~ 'big$uf'(sK0,X0,sK0)
| ~ 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| ~ 'big$uf'(sK4(sK0,sK0,X0),sK0,sK0) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ 'big$uf'(X0,sK0,sK0)
| ~ 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| ~ 'big$uf'(sK0,X0,sK0)
| ~ 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
( ~ 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,sK0,X0)
| ~ 'big$uf'(sK0,X0,sK0)
| ~ 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d11,c3]) ).
cnf(d13,plain,
( 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| ~ 'big$uf'(sK4(sK0,sK0,X0),sK0,sK0) ),
inference(resolution,[status(thm)],[d9,c5]) ).
cnf(d14,plain,
( 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,sK0,sK4(sK0,sK0,X0))
| 'big$uf'(sK0,X0,sK0) ),
inference(resolution,[status(thm)],[d13,d4]) ).
cnf(d15,plain,
( ~ 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,X0,sK0) ),
inference(resolution,[status(thm)],[d14,c4]) ).
cnf(d16,plain,
( 'big$uf'(sK0,sK4(sK0,sK0,X0),sK0)
| 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK0,sK4(sK0,sK0,X0),sK0) ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( ~ 'big$uf'(sK0,X0,sK0)
| 'big$uf'(X0,sK0,sK0)
| 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d16,c8]) ).
cnf(d18,plain,
( 'big$uf'(X0,sK0,sK0)
| 'big$uf'(sK4(sK0,sK0,X0),sK0,sK0) ),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
( 'big$uf'(sK0,sK0,X0)
| 'big$uf'(X0,sK0,sK0)
| 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d18,c11]) ).
cnf(d20,plain,
( 'big$uf'(sK0,X0,sK0)
| 'big$uf'(X0,sK0,sK0)
| 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
( 'big$uf'(sK0,X0,sK0)
| 'big$uf'(sK0,X0,sK0) ),
inference(resolution,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( 'big$uf'(sK0,sK0,X0)
| ~ 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d21,d12]) ).
cnf(d23,plain,
( 'big$uf'(X0,sK0,sK0)
| 'big$uf'(X0,sK0,sK0) ),
inference(resolution,[status(thm)],[d20,d17]) ).
cnf(d24,plain,
'big$uf'(sK0,sK0,X0),
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
( ~ 'big$uf'(X1,X2,X0)
| 'big$uf'(X2,X0,X1)
| 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d24,c0]) ).
cnf(d26,plain,
( 'big$uf'(X1,X2,X0)
| 'big$uf'(X1,X0,sK4(X0,X1,X2))
| 'big$uf'(sK4(X0,X1,X2),X1,X0) ),
inference(resolution,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
( ~ 'big$uf'(X2,X1,X0)
| ~ 'big$uf'(X0,X2,X1)
| 'big$uf'(X1,sK4(X1,X0,X2),X0)
| 'big$uf'(X0,X1,sK4(X1,X0,X2)) ),
inference(resolution,[status(thm)],[d25,c9]) ).
cnf(d28,plain,
( 'big$uf'(X1,X2,X0)
| ~ 'big$uf'(X2,X0,X1)
| 'big$uf'(X2,X1,sK4(X1,X2,X0))
| ~ 'big$uf'(X2,X0,X1)
| ~ 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d27,c7]) ).
cnf(d29,plain,
( ~ 'big$uf'(X1,X2,X0)
| 'big$uf'(X2,X0,X1)
| ~ 'big$uf'(X1,X2,X0)
| 'big$uf'(X2,X0,X1)
| ~ 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d28,c3]) ).
cnf(d30,plain,
( 'big$uf'(X0,X2,X1)
| ~ 'big$uf'(sK4(X1,X0,X2),X0,X1)
| 'big$uf'(X0,X1,sK4(X1,X0,X2)) ),
inference(resolution,[status(thm)],[d29,c5]) ).
cnf(d31,plain,
( 'big$uf'(X0,X2,sK4(X2,X0,X1))
| 'big$uf'(X0,X1,X2)
| 'big$uf'(X0,X2,sK4(X2,X0,X1))
| 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
( ~ 'big$uf'(X1,X2,X0)
| 'big$uf'(X0,X1,X2)
| 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d31,c4]) ).
cnf(d33,plain,
( 'big$uf'(X1,X2,X0)
| 'big$uf'(sK4(X0,X1,X2),X1,X0) ),
inference(resolution,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
( 'big$uf'(X2,X0,X1)
| 'big$uf'(X0,X1,X2)
| 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d33,c12]) ).
cnf(d35,plain,
( 'big$uf'(X0,X1,X2)
| 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
( ~ 'big$uf'(sK4(X2,X0,X1),sK4(X2,X0,X1),sK4(X2,X0,X1))
| ~ 'big$uf'(X2,X0,X1)
| ~ 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d35,c19]) ).
cnf(d37,plain,
( ~ 'big$uf'(sK4(X2,X0,X1),sK4(X2,X0,X1),sK4(X2,X0,X1))
| ~ 'big$uf'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d35,d36]) ).
cnf(d38,plain,
~ 'big$uf'(X0,X1,X2),
inference(resolution,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
$false,
inference(resolution,[status(thm)],[d35,d38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN353+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n003.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 17:39:09 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.71/1.92 % SZS status Theorem for theBenchmark.p
% 10.71/1.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------