%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET928+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 : n019.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 08:33:35 AM UTC 2026
% Result : Theorem 10.40s 1.78s
% Output : CNFRefutation 10.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 58 ( 24 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 52 ( 23 ~; 21 |; 5 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [X0,X1] : 'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
fof(t55_zfmisc_1,axiom,
! [X0,X1,X2] :
~ ( in(X0,X2)
& disjoint('unordered$upair'(X0,X1),X2) ) ).
fof(t57_zfmisc_1,axiom,
! [X0,X1,X2] :
~ ( ~ disjoint('unordered$upair'(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) ) ).
fof(t83_xboole_1,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> 'set$udifference'(X0,X1) = X0 ) ).
fof(t72_zfmisc_1,conjecture,
! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = 'unordered$upair'(X0,X1)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'set$udifference'('unordered$upair'(X0,X1),X2) = 'unordered$upair'(X0,X1)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ),
inference(negate_conjecture,[status(cth)],[t72_zfmisc_1]) ).
cnf(c1,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_tarski]) ).
cnf(c5,plain,
( ~ in(X0,X2)
| ~ disjoint('unordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[t55_zfmisc_1]) ).
cnf(c6,plain,
( disjoint('unordered$upair'(X0,X2),X1)
| in(X2,X1)
| in(X0,X1) ),
inference(clausification,[status(esa)],[t57_zfmisc_1]) ).
cnf(c7,plain,
( 'set$udifference'(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t83_xboole_1]) ).
cnf(c8,plain,
( 'set$udifference'(X0,X1) != X0
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t83_xboole_1]) ).
cnf(c10,plain,
( ~ in(sK16,sK18)
| 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11,plain,
( ~ in(sK17,sK18)
| 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
( 'set$udifference'('unordered$upair'(sK16,sK17),sK18) != 'unordered$upair'(sK16,sK17)
| in(sK17,sK18)
| in(sK16,sK18) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in(X0,X2)
| in(X1,X2)
| 'set$udifference'('unordered$upair'(X0,X1),X2) = 'unordered$upair'(X0,X1) ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d1,plain,
( 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17)
| in(X0,sK18)
| 'set$udifference'('unordered$upair'(X0,sK16),sK18) = 'unordered$upair'(X0,sK16) ),
inference(resolution,[status(thm)],[d0,c10]) ).
cnf(d2,plain,
( 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17)
| 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17)
| 'set$udifference'('unordered$upair'(sK17,sK16),sK18) = 'unordered$upair'(sK17,sK16) ),
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d3,plain,
( 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK17,sK16)
| 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17) ),
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17)
| 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17) ),
inference(demodulation,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
( 'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17)
| 'unordered$upair'(sK16,sK17) != 'unordered$upair'(sK16,sK17) ),
inference(equality_factoring,[status(thm)],[d4]) ).
cnf(d6,plain,
'set$udifference'('unordered$upair'(sK16,sK17),sK18) = 'unordered$upair'(sK16,sK17),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( in(sK17,sK18)
| in(sK16,sK18) ),
inference(resolution,[status(thm)],[d6,c12]) ).
cnf(d8,plain,
( ~ in(X0,X2)
| ~ disjoint('unordered$upair'(X1,X0),X2) ),
inference(superposition,[status(thm)],[c1,c5]) ).
cnf(d9,plain,
( disjoint('unordered$upair'(sK16,sK17),sK18)
| 'unordered$upair'(sK16,sK17) != 'unordered$upair'(sK16,sK17) ),
inference(superposition,[status(thm)],[d6,c8]) ).
cnf(d10,plain,
disjoint('unordered$upair'(sK16,sK17),sK18),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
~ in(sK17,sK18),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
in(sK16,sK18),
inference(resolution,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
~ in(sK16,sK18),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 08:26:04 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.40/1.78 % SZS status Theorem for theBenchmark.p
% 10.40/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------