%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET016+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 : n010.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 02:46:04 PM UTC 2026
% Result : Theorem 1.18s 1.28s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 107 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 39 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 76 !; 4 ?; 22 :)
% 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(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
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(f12,conjecture,
! [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
=> X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI50a) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
=> X0 = X2 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( equal_set(X0,X1)
=> ( subset(X1,X0)
& subset(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
& X0 != X2 ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| ( subset(X1,X0)
& subset(X0,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f19,plain,
( equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)))
& sK0 != sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ member(X0,singleton(X1))
| X0 = X1 )
& ( X0 != X1
| member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f23,plain,
equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))),
inference(cnf_transformation,[],[f19]) ).
fof(f24,plain,
sK0 != sK2,
inference(cnf_transformation,[],[f19]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f27,plain,
! [X2,X0,X1] :
( X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f29,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f27]) ).
fof(f35,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f29]) ).
tcf(c_49,negated_conjecture,
sK0 != sK2,
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,negated_conjecture,
equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))),
inference(cnf_transformation,[],[f23]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i] : member(X0,singleton(X0)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_59,plain,
member(sK0,singleton(sK0)),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ( unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)) != X1 )
| ( unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_57]) ).
tcf(c_128,plain,
subset(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
inference(unflattening,[status(thm)],[c_127]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ( unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)) != X0 )
| ( unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_128]) ).
tcf(c_140,plain,
! [X0: $i] :
( member(X0,unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))
| ~ member(X0,unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))) ),
inference(unflattening,[status(thm)],[c_139]) ).
tcf(c_161,plain,
! [X0: $i] :
( ~ member(X0,unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)))
| member(X0,unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))) ),
inference(prop_impl_just,[status(thm)],[c_140]) ).
tcf(c_162,plain,
! [X0: $i] :
( member(X0,unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))
| ~ member(X0,unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))) ),
inference(renaming,[status(thm)],[c_161]) ).
tcf(c_429,plain,
member(singleton(sK2),unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
inference(superposition,[status(thm)],[c_51,c_162]) ).
tcf(c_431,plain,
( ( singleton(sK0) = singleton(sK2) )
| ( unordered_pair(sK0,sK1) = singleton(sK2) ) ),
inference(superposition,[status(thm)],[c_429,c_53]) ).
tcf(c_439,plain,
( member(sK0,singleton(sK2))
| ( singleton(sK0) = singleton(sK2) ) ),
inference(superposition,[status(thm)],[c_431,c_51]) ).
tcf(c_477,plain,
( ( sK0 = sK2 )
| ( singleton(sK0) = singleton(sK2) ) ),
inference(superposition,[status(thm)],[c_439,c_55]) ).
tcf(c_478,plain,
singleton(sK0) = singleton(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_477,c_49]) ).
tcf(c_490,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ member(X0,singleton(sK0)) ),
inference(superposition,[status(thm)],[c_478,c_55]) ).
tcf(c_493,plain,
( ( sK0 = sK2 )
| ~ member(sK0,singleton(sK0)) ),
inference(instantiation,[status(thm)],[c_490]) ).
tcf(c_494,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_493,c_49,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 09:07:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.18/1.28 % SZS status Started for theBenchmark.p
% 1.18/1.28 % SZS status Theorem for theBenchmark.p
% 1.18/1.28
% 1.18/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.18/1.28
% 1.18/1.28 % ------ iProver source info
% 1.18/1.28
% 1.18/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.18/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.18/1.28 % git: non_committed_changes: false
% 1.18/1.28
% 1.18/1.28 % ------ Parsing...
% 1.18/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.18/1.28
% 1.18/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.18/1.28
% 1.18/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.18/1.28
% 1.18/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.18/1.28 % ------ Proving...
% 1.18/1.28 % ------ Problem Properties
% 1.18/1.28
% 1.18/1.28 %
% 1.18/1.28 % clauses 8
% 1.18/1.28 % conjectures 1
% 1.18/1.28 % EPR 1
% 1.18/1.28 % Horn 7
% 1.18/1.28 % unary 4
% 1.18/1.28 % binary 3
% 1.18/1.28 % lits 13
% 1.18/1.28 % lits eq 4
% 1.18/1.28 % fd_pure 0
% 1.18/1.28 % fd_pseudo 0
% 1.18/1.28 % fd_cond 0
% 1.18/1.28 % fd_pseudo_cond 2
% 1.18/1.28 % AC symbols 0
% 1.18/1.28
% 1.18/1.28 % ------ Schedule dynamic 5 is on
% 1.18/1.28
% 1.18/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.18/1.28
% 1.18/1.28
% 1.18/1.28 % ------
% 1.18/1.28 % Current options:
% 1.18/1.28 % ------
% 1.18/1.28
% 1.18/1.28
% 1.18/1.28 %
% 1.18/1.28
% 1.18/1.28 % ------ Proving...
% 1.18/1.28 %
% 1.18/1.28
% 1.18/1.28 % SZS status Theorem for theBenchmark.p
% 1.18/1.28
% 1.18/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.18/1.28
% 1.18/1.28
%------------------------------------------------------------------------------