%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET352+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 02:47:08 PM UTC 2026
% Result : Theorem 86.62s 14.47s
% Output : CNFRefutation 86.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 20 unt; 0 def)
% Number of atoms : 240 ( 58 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 263 ( 115 ~; 120 |; 19 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn 148 !; 6 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
fof(f9,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X2
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).
fof(f12,conjecture,
! [X0,X1] : equal_set(sum(unordered_pair(X0,X1)),union(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI40) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : equal_set(sum(unordered_pair(X0,X1)),union(X0,X1)),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0,X1] : ~ equal_set(sum(unordered_pair(X0,X1)),union(X0,X1)),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
~ equal_set(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 )
& ( ( X0 != X2
& X0 != X1 )
| member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 )
& ( ( X0 != X2
& X0 != X1 )
| member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ? [X2] :
( member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ? [X3] :
( member(X0,X3)
& member(X3,X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ( member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f19]) ).
fof(f29,plain,
~ equal_set(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X2,X0,X1] :
( X0 != X2
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
! [X2,X0,X1] :
( X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(X0,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f38,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f40,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f36]) ).
fof(f43,plain,
! [X2,X1] : member(X2,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f35]) ).
tcf(c_49,negated_conjecture,
~ equal_set(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f42]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : member(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,sum(X2))
| ~ member(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( member(sK2(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( member(X0,sK2(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_62,plain,
member(sK0,unordered_pair(sK0,sK0)),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_71,plain,
( ( sK0 = sK0 )
| ~ member(sK0,unordered_pair(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( union(sK0,sK1) != X1 )
| ( sum(unordered_pair(sK0,sK1)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).
tcf(c_181,plain,
( ~ subset(union(sK0,sK1),sum(unordered_pair(sK0,sK1)))
| ~ subset(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_180]) ).
tcf(c_292,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_294,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_646,plain,
( subset(sum(unordered_pair(sK0,sK1)),union(sK0,sK1))
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),union(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_647,plain,
( subset(sum(unordered_pair(sK0,sK1)),union(sK0,sK1))
| member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sum(unordered_pair(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_676,plain,
( subset(union(sK0,sK1),sum(unordered_pair(sK0,sK1)))
| member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),union(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_677,plain,
( subset(union(sK0,sK1),sum(unordered_pair(sK0,sK1)))
| ~ member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sum(unordered_pair(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_704,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,union(X1,X2))
| ~ member(sK3(X0,union(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_51,c_60]) ).
tcf(c_934,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(X0,unordered_pair(X1,X2)) = X2 )
| ( sK2(X0,unordered_pair(X1,X2)) = X1 )
| ~ member(X0,sum(unordered_pair(X1,X2))) ),
inference(superposition,[status(thm)],[c_58,c_56]) ).
tcf(c_1037,plain,
( member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)))
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sum(unordered_pair(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_2908,plain,
( member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sK1)
| member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sK0)
| ~ member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),union(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3072,plain,
sK1 = sK1,
inference(instantiation,[status(thm)],[c_292]) ).
tcf(c_10162,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)))
| ( X1 != sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( X0 != sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_298]) ).
tcf(c_11180,plain,
! [X0: $i] :
( member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sum(X0))
| ~ member(sK0,X0)
| ~ member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sK0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_20357,plain,
! [X0: $i,X1: $i] :
( member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),union(X0,X1))
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_20393,plain,
! [X0: $i] :
( member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sum(X0))
| ~ member(sK1,X0)
| ~ member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sK1) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_24594,plain,
( member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sum(unordered_pair(sK0,sK1)))
| ~ member(sK0,unordered_pair(sK0,sK1))
| ~ member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sK0) ),
inference(instantiation,[status(thm)],[c_11180]) ).
tcf(c_24930,plain,
( member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sum(unordered_pair(sK0,sK1)))
| ~ member(sK1,unordered_pair(sK0,sK1))
| ~ member(sK3(union(sK0,sK1),sum(unordered_pair(sK0,sK1))),sK1) ),
inference(instantiation,[status(thm)],[c_20393]) ).
tcf(c_26079,plain,
( member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),union(sK0,sK1))
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_20357]) ).
tcf(c_28083,plain,
! [X0: $i] : member(sK0,unordered_pair(sK0,X0)),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_29314,plain,
! [X0: $i] : member(sK1,unordered_pair(X0,sK1)),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_29315,plain,
member(sK1,unordered_pair(sK0,sK1)),
inference(instantiation,[status(thm)],[c_29314]) ).
tcf(c_36123,plain,
member(sK0,unordered_pair(sK0,sK1)),
inference(instantiation,[status(thm)],[c_28083]) ).
tcf(c_42427,plain,
! [X0: $i] :
( member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),X0)
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)))
| ( X0 != sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) != sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_10162]) ).
tcf(c_42428,plain,
sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) = sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),
inference(instantiation,[status(thm)],[c_292]) ).
tcf(c_42429,plain,
( member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK0)
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)))
| ( sK0 != sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) != sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_42427]) ).
tcf(c_47178,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( X1 != X0 )
| ( sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) != X0 ) ),
inference(instantiation,[status(thm)],[c_294]) ).
tcf(c_47179,plain,
( ( sK0 = sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( sK0 != sK0 )
| ( sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) != sK0 ) ),
inference(instantiation,[status(thm)],[c_47178]) ).
tcf(c_115411,plain,
( subset(sum(unordered_pair(sK0,sK1)),union(sK0,sK1))
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK1) ),
inference(instantiation,[status(thm)],[c_704]) ).
tcf(c_119586,plain,
! [X0: $i,X1: $i] :
( ( sK1 = X0 )
| ( sK1 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_294]) ).
tcf(c_177509,plain,
! [X0: $i] :
( ( sK1 = X0 )
| ( sK1 != sK1 )
| ( X0 != sK1 ) ),
inference(instantiation,[status(thm)],[c_119586]) ).
tcf(c_190256,plain,
( ( sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) = sK1 )
| ( sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) = sK0 )
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sum(unordered_pair(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_934]) ).
tcf(c_206239,plain,
( ( sK1 = sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( sK1 != sK1 )
| ( sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) != sK1 ) ),
inference(instantiation,[status(thm)],[c_177509]) ).
tcf(c_226584,plain,
~ subset(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_181,c_181,c_677,c_676,c_2908,c_24594,c_24930,c_29315,c_36123]) ).
tcf(c_237980,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)))
| ( X1 != sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( X0 != sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_298]) ).
tcf(c_298593,plain,
! [X0: $i] :
( member(X0,sK1)
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)))
| ( sK1 != sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( X0 != sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_237980]) ).
tcf(c_310238,plain,
( member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK1)
| ~ member(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)))
| ( sK1 != sK2(sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)),unordered_pair(sK0,sK1)) )
| ( sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) != sK3(sum(unordered_pair(sK0,sK1)),union(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_298593]) ).
tcf(c_310239,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_310238,c_226584,c_206239,c_190256,c_115411,c_47179,c_42428,c_42429,c_26079,c_3072,c_1037,c_647,c_646,c_71,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET352+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n011.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Thu Sep 24 10:40:58 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 86.62/14.47 % SZS status Started for theBenchmark.p
% 86.62/14.47 % SZS status Theorem for theBenchmark.p
% 86.62/14.47
% 86.62/14.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 86.62/14.47
% 86.62/14.47 % ------ iProver source info
% 86.62/14.47
% 86.62/14.47 % git: date: 2026-07-19 20:42:38 +0200
% 86.62/14.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 86.62/14.47 % git: non_committed_changes: false
% 86.62/14.47
% 86.62/14.47 % ------ Parsing...
% 86.62/14.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 86.62/14.47
% 86.62/14.47 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 86.62/14.47
% 86.62/14.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 86.62/14.47
% 86.62/14.47 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 86.62/14.47 % ------ Proving...
% 86.62/14.47 % ------ Problem Properties
% 86.62/14.47
% 86.62/14.47 %
% 86.62/14.47 % clauses 12
% 86.62/14.47 % conjectures 0
% 86.62/14.47 % EPR 0
% 86.62/14.47 % Horn 9
% 86.62/14.47 % unary 2
% 86.62/14.47 % binary 7
% 86.62/14.47 % lits 25
% 86.62/14.47 % lits eq 2
% 86.62/14.47 % fd_pure 0
% 86.62/14.47 % fd_pseudo 0
% 86.62/14.47 % fd_cond 0
% 86.62/14.47 % fd_pseudo_cond 1
% 86.62/14.47 % AC symbols 0
% 86.62/14.47
% 86.62/14.47 % ------ Schedule dynamic 5 is on
% 86.62/14.47
% 86.62/14.47 % ------ no conjectures: strip conj schedule
% 86.62/14.47
% 86.62/14.47 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 86.62/14.47
% 86.62/14.47
% 86.62/14.47 % ------
% 86.62/14.47 % Current options:
% 86.62/14.47 % ------
% 86.62/14.47
% 86.62/14.47
% 86.62/14.47 %
% 86.62/14.47
% 86.62/14.47 % ------ Proving...
% 86.62/14.47 % Proof_search_loop: time out after: 5220 full_loop iterations
% 86.62/14.47
% 86.62/14.47 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" stripped conjectures Time Limit: 15.
% 86.62/14.47
% 86.62/14.47
% 86.62/14.47 % ------
% 86.62/14.47 % Current options:
% 86.62/14.47 % ------
% 86.62/14.47
% 86.62/14.47
% 86.62/14.47 %
% 86.62/14.47
% 86.62/14.47 % ------ Proving...
% 86.62/14.47 %
% 86.62/14.47
% 86.62/14.47 % SZS status Theorem for theBenchmark.p
% 86.62/14.47
% 86.62/14.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 86.62/14.47
% 86.62/14.47
%------------------------------------------------------------------------------