%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:31:36 AM UTC 2026
% Result : Unsatisfiable 8.81s 16.92s
% Output : CNFRefutation 8.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of clauses : 49 ( 19 unt; 27 nHn; 39 RR)
% Number of literals : 94 ( 68 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(singleton_1,axiom,
member(X0,'singleton$uset'(X0)) ).
cnf(singleton_2,axiom,
( X0 = X1
| ~ member(X0,'singleton$uset'(X1)) ) ).
cnf(unordered_pair_1,axiom,
member(X0,'unordered$upair'(X0,X1)) ).
cnf(unordered_pair_2,axiom,
member(X0,'unordered$upair'(X1,X0)) ).
cnf(unordered_pair_3,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(ordered_pair,axiom,
'ordered$upair'(X0,X1) = 'unordered$upair'('singleton$uset'(X0),'unordered$upair'(X0,X1)) ).
cnf(equal_ordered_pairs,hypothesis,
'ordered$upair'(m1,r1) = 'ordered$upair'(m2,r2) ).
cnf(prove_second_components_equal,negated_conjecture,
r1 != r2 ).
cnf(c0,plain,
member(X0,'singleton$uset'(X0)),
inference(clausification,[status(esa)],[singleton_1]) ).
cnf(c1,plain,
( X0 = X1
| ~ member(X0,'singleton$uset'(X1)) ),
inference(clausification,[status(esa)],[singleton_2]) ).
cnf(c2,plain,
member(X0,'unordered$upair'(X0,X1)),
inference(clausification,[status(esa)],[unordered_pair_1]) ).
cnf(c3,plain,
member(X0,'unordered$upair'(X1,X0)),
inference(clausification,[status(esa)],[unordered_pair_2]) ).
cnf(c4,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_3]) ).
cnf(c5,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'('singleton$uset'(X0),'unordered$upair'(X0,X1)),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(c6,plain,
'ordered$upair'(m1,r1) = 'ordered$upair'(m2,r2),
inference(clausification,[status(esa)],[equal_ordered_pairs]) ).
cnf(c7,plain,
r1 != r2,
inference(clausification,[status(esa)],[prove_second_components_equal]) ).
cnf(d0,plain,
member('singleton$uset'(X0),'ordered$upair'(X0,X1)),
inference(superposition,[status(thm)],[c5,c2]) ).
cnf(d1,plain,
member('singleton$uset'(m2),'ordered$upair'(m1,r1)),
inference(superposition,[status(thm)],[c6,d0]) ).
cnf(d2,plain,
( X2 = 'singleton$uset'(X0)
| X2 = 'unordered$upair'(X0,X1)
| ~ member(X2,'ordered$upair'(X0,X1)) ),
inference(superposition,[status(thm)],[c5,c4]) ).
cnf(d3,plain,
( 'singleton$uset'(m2) = 'unordered$upair'(m1,r1)
| 'singleton$uset'(m2) = 'singleton$uset'(m1) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( 'singleton$uset'(m2) = 'singleton$uset'(m1)
| member(m1,'singleton$uset'(m2)) ),
inference(superposition,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( m1 = m2
| 'singleton$uset'(m2) = 'singleton$uset'(m1) ),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
( m1 = m2
| member(m2,'singleton$uset'(m1)) ),
inference(superposition,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
( m2 = m1
| m1 = m2 ),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
( m2 = m1
| m1 != m1 ),
inference(equality_factoring,[status(thm)],[d7]) ).
cnf(d9,plain,
m2 = m1,
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
member('unordered$upair'(X0,X1),'ordered$upair'(X0,X1)),
inference(superposition,[status(thm)],[c5,c3]) ).
cnf(d11,plain,
( X0 = 'unordered$upair'(m2,r2)
| X0 = 'singleton$uset'(m2)
| ~ member(X0,'ordered$upair'(m1,r1)) ),
inference(superposition,[status(thm)],[c6,d2]) ).
cnf(d12,plain,
( 'unordered$upair'(m1,r1) = 'unordered$upair'(m2,r2)
| 'unordered$upair'(m1,r1) = 'singleton$uset'(m2) ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( 'unordered$upair'(m1,r1) = 'unordered$upair'(m2,r2)
| 'unordered$upair'(m1,r1) = 'singleton$uset'(m1) ),
inference(demodulation,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
( 'unordered$upair'(m1,r1) = 'unordered$upair'(m1,r2)
| 'unordered$upair'(m1,r1) = 'singleton$uset'(m1) ),
inference(demodulation,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
member('unordered$upair'(m2,r2),'ordered$upair'(m1,r1)),
inference(superposition,[status(thm)],[c6,d10]) ).
cnf(d16,plain,
( 'unordered$upair'(m2,r2) = 'unordered$upair'(m1,r1)
| 'unordered$upair'(m2,r2) = 'singleton$uset'(m1) ),
inference(resolution,[status(thm)],[d15,d2]) ).
cnf(d17,plain,
( 'unordered$upair'(m2,r2) = 'singleton$uset'(m1)
| X0 = m2
| X0 = r2
| ~ member(X0,'unordered$upair'(m1,r1)) ),
inference(superposition,[status(thm)],[d16,c4]) ).
cnf(d18,plain,
( ~ member(X0,'unordered$upair'(m1,r1))
| 'unordered$upair'(m2,r2) = 'singleton$uset'(m1)
| X0 = r2
| X0 = m1 ),
inference(demodulation,[status(thm)],[d17,d9]) ).
cnf(d19,plain,
( ~ member(X0,'unordered$upair'(m1,r1))
| 'unordered$upair'(m1,r2) = 'singleton$uset'(m1)
| X0 = r2
| X0 = m1 ),
inference(demodulation,[status(thm)],[d18,d9]) ).
cnf(d20,plain,
( 'unordered$upair'(m1,r2) = 'singleton$uset'(m1)
| r1 = r2
| r1 = m1 ),
inference(resolution,[status(thm)],[d19,c3]) ).
cnf(d21,plain,
( r1 = m1
| 'unordered$upair'(m1,r2) = 'singleton$uset'(m1) ),
inference(resolution,[status(thm)],[c7,d20]) ).
cnf(d22,plain,
( r1 = m1
| 'unordered$upair'(m1,r1) = 'singleton$uset'(m1)
| 'unordered$upair'(m1,r1) = 'singleton$uset'(m1) ),
inference(superposition,[status(thm)],[d21,d14]) ).
cnf(d23,plain,
( r1 = m1
| member(r1,'singleton$uset'(m1)) ),
inference(superposition,[status(thm)],[d22,c3]) ).
cnf(d24,plain,
( r1 = m1
| r1 = m1 ),
inference(resolution,[status(thm)],[d23,c1]) ).
cnf(d25,plain,
( 'unordered$upair'(m2,r2) = 'singleton$uset'(m1)
| member(r2,'unordered$upair'(m1,r1)) ),
inference(superposition,[status(thm)],[d16,c3]) ).
cnf(d26,plain,
( member(r2,'unordered$upair'(m1,r1))
| 'unordered$upair'(m1,r2) = 'singleton$uset'(m1) ),
inference(demodulation,[status(thm)],[d25,d9]) ).
cnf(d27,plain,
( r2 = m1
| r2 = r1
| 'unordered$upair'(m1,r2) = 'singleton$uset'(m1) ),
inference(resolution,[status(thm)],[d26,c4]) ).
cnf(d28,plain,
( r2 = r1
| r2 = m1
| member(r2,'singleton$uset'(m1)) ),
inference(superposition,[status(thm)],[d27,c3]) ).
cnf(d29,plain,
( r2 = m1
| r2 = r1
| r2 = m1 ),
inference(resolution,[status(thm)],[d28,c1]) ).
cnf(d30,plain,
( r2 = r1
| r2 = r1 ),
inference(demodulation,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
r1 != r1,
inference(demodulation,[status(thm)],[c7,d30]) ).
cnf(d32,plain,
$false,
inference(equality_resolution,[status(thm)],[d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/15.47 % CPULimit : 300
% 0.08/15.47 % WCLimit : 300
% 0.08/15.47 % DateTime : Sat Sep 26 06:51:51 UTC 2026
% 0.08/15.47 % CPUTime :
% 0.08/15.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.81/16.92 % SZS status Unsatisfiable for theBenchmark.p
% 8.81/16.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------