%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU156+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:41:04 AM UTC 2026
% Result : Theorem 15.01s 7.39s
% Output : CNFRefutation 15.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 19 unt; 0 def)
% Number of atoms : 174 ( 173 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 145 ( 50 ~; 87 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 13 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [X0,X1] : 'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
fof(d5_tarski,axiom,
! [X0,X1] : 'ordered$upair'(X0,X1) = 'unordered$upair'('unordered$upair'(X0,X1),singleton(X0)) ).
fof(t10_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& 'unordered$upair'(X0,X1) = 'unordered$upair'(X2,X3) ) ).
fof(t69_enumset1,axiom,
! [X0] : 'unordered$upair'(X0,X0) = singleton(X0) ).
fof(t8_zfmisc_1,axiom,
! [X0,X1,X2] :
( singleton(X0) = 'unordered$upair'(X1,X2)
=> X0 = X1 ) ).
fof(t9_zfmisc_1,axiom,
! [X0,X1,X2] :
( singleton(X0) = 'unordered$upair'(X1,X2)
=> X1 = X2 ) ).
fof(t33_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( 'ordered$upair'(X0,X1) = 'ordered$upair'(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( 'ordered$upair'(X0,X1) = 'ordered$upair'(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
inference(negate_conjecture,[status(cth)],[t33_zfmisc_1]) ).
cnf(c0,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_tarski]) ).
cnf(c1,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'('unordered$upair'(X0,X1),singleton(X0)),
inference(clausification,[status(esa)],[d5_tarski]) ).
cnf(c6,plain,
( X0 = X3
| X0 = X2
| 'unordered$upair'(X0,X1) != 'unordered$upair'(X2,X3) ),
inference(clausification,[status(esa)],[t10_zfmisc_1]) ).
cnf(c7,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[t69_enumset1]) ).
cnf(c9,plain,
( X0 = X1
| singleton(X0) != 'unordered$upair'(X1,X2) ),
inference(clausification,[status(esa)],[t8_zfmisc_1]) ).
cnf(c10,plain,
( X1 = X2
| singleton(X0) != 'unordered$upair'(X1,X2) ),
inference(clausification,[status(esa)],[t9_zfmisc_1]) ).
cnf(c11,plain,
'ordered$upair'(sK23,sK24) = 'ordered$upair'(sK25,sK26),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
( sK24 != sK26
| sK23 != sK25 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( X0 = X1
| singleton(X2) != 'unordered$upair'(X1,X0) ),
inference(superposition,[status(thm)],[c0,c10]) ).
cnf(d1,plain,
( X1 = X0
| singleton(X1) != singleton(X0) ),
inference(superposition,[status(thm)],[c7,c9]) ).
cnf(d2,plain,
( X1 = X0
| X1 = X0
| 'unordered$upair'(X1,X2) != singleton(X0) ),
inference(superposition,[status(thm)],[c7,c6]) ).
cnf(d3,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c0]) ).
cnf(d4,plain,
( singleton(X0) = X2
| singleton(X0) = X3
| 'ordered$upair'(X0,X1) != 'unordered$upair'(X2,X3) ),
inference(superposition,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( singleton(sK25) = X0
| singleton(sK25) = X1
| 'ordered$upair'(sK23,sK24) != 'unordered$upair'(X0,X1) ),
inference(superposition,[status(thm)],[c11,d4]) ).
cnf(d6,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X1,X0)),
inference(superposition,[status(thm)],[c0,d3]) ).
cnf(d7,plain,
( singleton(sK25) = singleton(X0)
| singleton(sK25) = 'unordered$upair'(X1,X0)
| 'ordered$upair'(sK23,sK24) != 'ordered$upair'(X0,X1) ),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( singleton(sK25) = singleton(sK23)
| singleton(sK25) = 'unordered$upair'(sK24,sK23) ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( singleton(sK25) = singleton(sK23)
| singleton(sK25) = 'unordered$upair'(sK23,sK24) ),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
( singleton(sK25) = singleton(sK23)
| sK23 = X0
| singleton(sK25) != singleton(X0) ),
inference(superposition,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( sK23 = sK25
| singleton(sK25) = singleton(sK23) ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( sK23 = sK25
| sK25 = X0
| singleton(sK23) != singleton(X0) ),
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( sK25 = sK23
| sK23 = sK25 ),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( sK25 = sK23
| sK23 != sK23 ),
inference(equality_factoring,[status(thm)],[d13]) ).
cnf(d15,plain,
sK25 = sK23,
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( X2 = singleton(X0)
| X2 = 'unordered$upair'(X0,X1)
| 'unordered$upair'(X2,X3) != 'ordered$upair'(X0,X1) ),
inference(superposition,[status(thm)],[d3,c6]) ).
cnf(d17,plain,
( X0 = singleton(sK25)
| X0 = 'unordered$upair'(sK25,sK26)
| 'unordered$upair'(X0,X1) != 'ordered$upair'(sK23,sK24) ),
inference(superposition,[status(thm)],[c11,d16]) ).
cnf(d18,plain,
( X0 = singleton(sK25)
| X0 = 'unordered$upair'(sK25,sK26)
| 'unordered$upair'(X1,X0) != 'ordered$upair'(sK23,sK24) ),
inference(superposition,[status(thm)],[c0,d17]) ).
cnf(d19,plain,
( 'unordered$upair'(X1,X0) = singleton(sK25)
| 'unordered$upair'(X1,X0) = 'unordered$upair'(sK25,sK26)
| 'ordered$upair'(X0,X1) != 'ordered$upair'(sK23,sK24) ),
inference(superposition,[status(thm)],[d6,d18]) ).
cnf(d20,plain,
( 'ordered$upair'(X1,X0) != 'ordered$upair'(sK23,sK24)
| 'unordered$upair'(X0,X1) = singleton(sK25)
| 'unordered$upair'(X0,X1) = 'unordered$upair'(sK23,sK26) ),
inference(demodulation,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
( 'ordered$upair'(X1,X0) != 'ordered$upair'(sK23,sK24)
| 'unordered$upair'(X0,X1) = singleton(sK23)
| 'unordered$upair'(X0,X1) = 'unordered$upair'(sK23,sK26) ),
inference(demodulation,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( 'unordered$upair'(sK24,sK23) = singleton(sK23)
| 'unordered$upair'(sK24,sK23) = 'unordered$upair'(sK23,sK26) ),
inference(equality_resolution,[status(thm)],[d21]) ).
cnf(d23,plain,
( 'unordered$upair'(sK24,sK23) = singleton(sK23)
| 'unordered$upair'(sK23,sK24) = 'unordered$upair'(sK23,sK26) ),
inference(demodulation,[status(thm)],[d22,c0]) ).
cnf(d24,plain,
( 'unordered$upair'(sK23,sK24) = singleton(sK23)
| 'unordered$upair'(sK23,sK24) = 'unordered$upair'(sK23,sK26) ),
inference(demodulation,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
( X0 = X2
| X0 = X3
| 'unordered$upair'(X1,X0) != 'unordered$upair'(X2,X3) ),
inference(superposition,[status(thm)],[c0,c6]) ).
cnf(d26,plain,
( 'unordered$upair'(X1,X0) = X2
| 'unordered$upair'(X1,X0) = X3
| 'ordered$upair'(X0,X1) != 'unordered$upair'(X2,X3) ),
inference(superposition,[status(thm)],[d6,d25]) ).
cnf(d27,plain,
'ordered$upair'(sK23,sK24) = 'ordered$upair'(sK23,sK26),
inference(demodulation,[status(thm)],[c11,d15]) ).
cnf(d28,plain,
( 'unordered$upair'(sK26,sK23) = X0
| 'unordered$upair'(sK26,sK23) = X1
| 'ordered$upair'(sK23,sK24) != 'unordered$upair'(X0,X1) ),
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( 'ordered$upair'(sK23,sK24) != 'unordered$upair'(X1,X0)
| 'unordered$upair'(sK26,sK23) = X1
| 'unordered$upair'(sK23,sK26) = X0 ),
inference(demodulation,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
( 'ordered$upair'(sK23,sK24) != 'unordered$upair'(X1,X0)
| 'unordered$upair'(sK23,sK26) = X1
| 'unordered$upair'(sK23,sK26) = X0 ),
inference(demodulation,[status(thm)],[d29,c0]) ).
cnf(d31,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(superposition,[status(thm)],[c7,c0]) ).
cnf(d32,plain,
( 'unordered$upair'(sK23,sK26) = X0
| 'unordered$upair'(sK23,sK26) = X0
| 'ordered$upair'(sK23,sK24) != singleton(X0) ),
inference(superposition,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
'ordered$upair'(X0,X0) = 'unordered$upair'(singleton(X0),singleton(X0)),
inference(superposition,[status(thm)],[c7,d3]) ).
cnf(d34,plain,
'ordered$upair'(X0,X0) = singleton(singleton(X0)),
inference(demodulation,[status(thm)],[d33,c7]) ).
cnf(d35,plain,
( sK24 != sK26
| sK23 != sK23 ),
inference(demodulation,[status(thm)],[c12,d15]) ).
cnf(d36,plain,
( X2 = X0
| X2 = X0
| 'unordered$upair'(X1,X2) != singleton(X0) ),
inference(superposition,[status(thm)],[d31,d25]) ).
cnf(d37,plain,
( 'unordered$upair'(sK23,sK24) = singleton(sK23)
| sK26 = X0
| sK26 = X1
| 'unordered$upair'(sK23,sK24) != 'unordered$upair'(X0,X1) ),
inference(superposition,[status(thm)],[d24,d25]) ).
cnf(d38,plain,
( sK26 = sK23
| sK26 = sK24
| 'unordered$upair'(sK23,sK24) = singleton(sK23) ),
inference(equality_resolution,[status(thm)],[d37]) ).
cnf(d39,plain,
( sK26 = sK24
| sK26 = sK23
| sK24 = X0
| singleton(sK23) != singleton(X0) ),
inference(superposition,[status(thm)],[d38,d36]) ).
cnf(d40,plain,
( sK26 = sK24
| sK26 = sK23
| sK24 = sK23 ),
inference(equality_resolution,[status(thm)],[d39]) ).
cnf(d41,plain,
( sK26 = sK23
| sK24 = sK23
| sK23 != sK23
| sK24 != sK24 ),
inference(superposition,[status(thm)],[d40,d35]) ).
cnf(d42,plain,
( sK26 = sK23
| sK24 = sK23
| sK23 != sK23 ),
inference(equality_resolution,[status(thm)],[d41]) ).
cnf(d43,plain,
( sK26 = sK23
| sK24 = sK23 ),
inference(equality_resolution,[status(thm)],[d42]) ).
cnf(d44,plain,
( sK24 = sK23
| 'ordered$upair'(sK23,sK24) = 'ordered$upair'(sK23,sK23) ),
inference(superposition,[status(thm)],[d43,d27]) ).
cnf(d45,plain,
( sK24 = sK23
| 'ordered$upair'(sK23,sK24) = singleton(singleton(sK23)) ),
inference(demodulation,[status(thm)],[d44,d34]) ).
cnf(d46,plain,
( sK24 = sK23
| 'unordered$upair'(sK23,sK26) = X0
| singleton(singleton(sK23)) != singleton(X0) ),
inference(superposition,[status(thm)],[d45,d32]) ).
cnf(d47,plain,
( sK24 = sK23
| 'unordered$upair'(sK23,sK26) = singleton(sK23) ),
inference(equality_resolution,[status(thm)],[d46]) ).
cnf(d48,plain,
( sK24 = sK23
| 'unordered$upair'(sK23,sK24) = singleton(sK23)
| 'unordered$upair'(sK23,sK24) = singleton(sK23) ),
inference(superposition,[status(thm)],[d47,d24]) ).
cnf(d49,plain,
( sK24 = sK23
| sK24 = sK23
| singleton(X0) != singleton(sK23) ),
inference(superposition,[status(thm)],[d48,d0]) ).
cnf(d50,plain,
sK24 = sK23,
inference(equality_resolution,[status(thm)],[d49]) ).
cnf(d51,plain,
( sK23 != sK26
| sK23 != sK23 ),
inference(demodulation,[status(thm)],[d35,d50]) ).
cnf(d52,plain,
( X2 = X0
| singleton(X2) != 'unordered$upair'(X1,X0) ),
inference(superposition,[status(thm)],[c0,c9]) ).
cnf(d53,plain,
( X2 = 'unordered$upair'(X1,X0)
| singleton(X2) != 'ordered$upair'(X0,X1) ),
inference(superposition,[status(thm)],[d6,d52]) ).
cnf(d54,plain,
( X0 = 'unordered$upair'(sK26,sK23)
| singleton(X0) != 'ordered$upair'(sK23,sK24) ),
inference(superposition,[status(thm)],[d27,d53]) ).
cnf(d55,plain,
( singleton(X0) != 'ordered$upair'(sK23,sK24)
| X0 = 'unordered$upair'(sK23,sK26) ),
inference(demodulation,[status(thm)],[d54,c0]) ).
cnf(d56,plain,
( singleton(X0) != 'ordered$upair'(sK23,sK23)
| X0 = 'unordered$upair'(sK23,sK26) ),
inference(demodulation,[status(thm)],[d55,d50]) ).
cnf(d57,plain,
( singleton(X0) != singleton(singleton(sK23))
| X0 = 'unordered$upair'(sK23,sK26) ),
inference(demodulation,[status(thm)],[d56,d34]) ).
cnf(d58,plain,
singleton(sK23) = 'unordered$upair'(sK23,sK26),
inference(equality_resolution,[status(thm)],[d57]) ).
cnf(d59,plain,
( X0 = sK26
| singleton(X0) != singleton(sK23) ),
inference(superposition,[status(thm)],[d58,d52]) ).
cnf(d60,plain,
sK23 = sK26,
inference(equality_resolution,[status(thm)],[d59]) ).
cnf(d61,plain,
sK23 != sK23,
inference(resolution,[status(thm)],[d60,d51]) ).
cnf(d62,plain,
$false,
inference(equality_resolution,[status(thm)],[d61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.39 % Computer : n015.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Sat Sep 26 08:44:48 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.01/7.39 % SZS status Theorem for theBenchmark.p
% 15.01/7.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------