%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 08:32:04 AM UTC 2026
% Result : Unsatisfiable 37.23s 20.93s
% Output : CNFRefutation 37.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 38 ( 34 unt; 4 nHn; 17 RR)
% Number of literals : 42 ( 33 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair_equals_singleton2,axiom,
( 'unordered$upair'(X0,X1) = singleton(X1)
| member(X0,'universal$uclass') ) ).
cnf(singleton_is_null_class,axiom,
( singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ) ).
cnf(unordered_pairs_and_singletons,axiom,
'unordered$upair'(X0,X1) = union(singleton(X0),singleton(X1)) ).
cnf(prove_property_3_of_ordered_pair_1,negated_conjecture,
'unordered$upair'('null$uclass',singleton('null$uclass')) != 'ordered$upair'(x,y) ).
cnf(prove_property_3_of_ordered_pair_2,negated_conjecture,
~ member(x,'universal$uclass') ).
cnf(prove_property_3_of_ordered_pair_3,negated_conjecture,
~ member(y,'universal$uclass') ).
cnf(ordered_pair,axiom,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1) ).
cnf(successor,axiom,
union(X0,singleton(X0)) = successor(X0) ).
cnf(c20,plain,
( 'unordered$upair'(X0,X1) = singleton(X1)
| member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair_equals_singleton2]) ).
cnf(c34,plain,
( singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[singleton_is_null_class]) ).
cnf(c52,plain,
'unordered$upair'(X0,X1) = union(singleton(X0),singleton(X1)),
inference(clausification,[status(esa)],[unordered_pairs_and_singletons]) ).
cnf(c56,plain,
'unordered$upair'('null$uclass',singleton('null$uclass')) != 'ordered$upair'(x,y),
inference(clausification,[status(esa)],[prove_property_3_of_ordered_pair_1]) ).
cnf(c57,plain,
~ member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_property_3_of_ordered_pair_2]) ).
cnf(c58,plain,
~ member(y,'universal$uclass'),
inference(clausification,[status(esa)],[prove_property_3_of_ordered_pair_3]) ).
cnf(c71,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(c101,plain,
union(X0,singleton(X0)) = successor(X0),
inference(clausification,[status(esa)],[successor]) ).
cnf(d0,plain,
'unordered$upair'(X0,singleton(X0)) = successor(singleton(X0)),
inference(superposition,[status(thm)],[c101,c52]) ).
cnf(d1,plain,
'unordered$upair'(x,X0) = singleton(X0),
inference(resolution,[status(thm)],[c20,c57]) ).
cnf(d2,plain,
singleton(x) = 'null$uclass',
inference(resolution,[status(thm)],[c34,c57]) ).
cnf(d3,plain,
'unordered$upair'('null$uclass','unordered$upair'(x,singleton(X0))) = 'ordered$upair'(x,X0),
inference(superposition,[status(thm)],[d2,c71]) ).
cnf(d4,plain,
'unordered$upair'('null$uclass',singleton(singleton(X0))) = 'ordered$upair'(x,X0),
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
'unordered$upair'('null$uclass',singleton('null$uclass')) = 'ordered$upair'(x,x),
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
successor(singleton('null$uclass')) = 'ordered$upair'(x,x),
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,'null$uclass')) = 'ordered$upair'(X0,x),
inference(superposition,[status(thm)],[d2,c71]) ).
cnf(d8,plain,
singleton(y) = 'null$uclass',
inference(resolution,[status(thm)],[c34,c58]) ).
cnf(d9,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,'null$uclass')) = 'ordered$upair'(X0,y),
inference(superposition,[status(thm)],[d8,c71]) ).
cnf(d10,plain,
'ordered$upair'(X0,x) = 'ordered$upair'(X0,y),
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
'unordered$upair'('null$uclass',singleton('null$uclass')) != 'ordered$upair'(x,x),
inference(demodulation,[status(thm)],[c56,d10]) ).
cnf(d12,plain,
successor(singleton('null$uclass')) != 'ordered$upair'(x,x),
inference(demodulation,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
'ordered$upair'(x,x) != 'ordered$upair'(x,x),
inference(demodulation,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
'unordered$upair'(y,X0) = singleton(X0),
inference(resolution,[status(thm)],[c20,c58]) ).
cnf(d15,plain,
'unordered$upair'('null$uclass','unordered$upair'(y,singleton(X0))) = 'ordered$upair'(y,X0),
inference(superposition,[status(thm)],[d8,c71]) ).
cnf(d16,plain,
'unordered$upair'('null$uclass',singleton(singleton(X0))) = 'ordered$upair'(y,X0),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
'ordered$upair'(x,X0) = 'ordered$upair'(y,X0),
inference(demodulation,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
'ordered$upair'(x,y) = 'ordered$upair'(y,x),
inference(superposition,[status(thm)],[d10,d17]) ).
cnf(d19,plain,
'ordered$upair'(x,x) = 'ordered$upair'(y,x),
inference(demodulation,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
'ordered$upair'(x,x) = 'ordered$upair'(x,x),
inference(demodulation,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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
% 0.09/15.57 % CPULimit : 300
% 0.09/15.57 % WCLimit : 300
% 0.09/15.57 % DateTime : Sat Sep 26 07:09:20 UTC 2026
% 0.09/15.58 % CPUTime :
% 0.09/15.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.23/20.93 % SZS status Unsatisfiable for theBenchmark.p
% 37.23/20.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------