%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET018+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 : n012.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 02:46:05 PM UTC 2026
% Result : Theorem 3.50s 1.06s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 77 ( 24 unt; 0 def)
% Number of atoms : 160 ( 67 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 49 ~; 63 |; 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 : 99 ( 0 sgn 95 !; 4 ?; 34 :)
% 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)))
=> X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI50b) ).
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)))
=> X1 = X3 ),
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)))
& X1 != X3 ),
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)))
& sK1 != sK3 ),
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,
sK1 != sK3,
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(f26,plain,
! [X2,X0,X1] :
( X0 != X2
| member(X0,unordered_pair(X1,X2)) ),
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(f31,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
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(f34,plain,
! [X2,X1] : member(X2,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f26]) ).
fof(f35,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f29]) ).
tcf(c_49,negated_conjecture,
sK1 != sK3,
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_52,plain,
! [X0: $i,X1: $i] : member(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f34]) ).
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_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
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_132,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( 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_56]) ).
tcf(c_133,plain,
subset(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))),
inference(unflattening,[status(thm)],[c_132]) ).
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_148,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,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_58,c_133]) ).
tcf(c_149,plain,
! [X0: $i] :
( member(X0,unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)))
| ~ member(X0,unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))) ),
inference(unflattening,[status(thm)],[c_148]) ).
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_163,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_149]) ).
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_430,plain,
member(unordered_pair(sK2,sK3),unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
inference(superposition,[status(thm)],[c_52,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_455,plain,
member(unordered_pair(sK0,sK1),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))),
inference(superposition,[status(thm)],[c_52,c_163]) ).
tcf(c_477,plain,
( ( sK0 = sK2 )
| ( singleton(sK0) = singleton(sK2) ) ),
inference(superposition,[status(thm)],[c_439,c_55]) ).
tcf(c_506,plain,
( member(sK2,singleton(sK0))
| ( sK0 = sK2 ) ),
inference(superposition,[status(thm)],[c_477,c_54]) ).
tcf(c_507,plain,
! [X0: $i] :
( ( sK0 = sK2 )
| ( X0 = sK2 )
| ~ member(X0,singleton(sK0)) ),
inference(superposition,[status(thm)],[c_477,c_55]) ).
tcf(c_518,plain,
( ( sK0 = sK2 )
| ~ member(sK0,singleton(sK0)) ),
inference(instantiation,[status(thm)],[c_507]) ).
tcf(c_520,plain,
sK0 = sK2,
inference(global_subsumption_just,[status(thm)],[c_506,c_59,c_518]) ).
tcf(c_523,plain,
member(unordered_pair(sK0,sK1),unordered_pair(singleton(sK0),unordered_pair(sK0,sK3))),
inference(demodulation,[status(thm)],[c_455,c_520]) ).
tcf(c_526,plain,
member(unordered_pair(sK0,sK3),unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
inference(demodulation,[status(thm)],[c_430,c_520]) ).
tcf(c_543,plain,
( ( unordered_pair(sK0,sK1) = singleton(sK0) )
| ( unordered_pair(sK0,sK1) = unordered_pair(sK0,sK3) ) ),
inference(superposition,[status(thm)],[c_523,c_53]) ).
tcf(c_568,plain,
( member(sK3,unordered_pair(sK0,sK1))
| ( unordered_pair(sK0,sK1) = singleton(sK0) ) ),
inference(superposition,[status(thm)],[c_543,c_52]) ).
tcf(c_582,plain,
( ( sK3 = sK0 )
| ( sK1 = sK3 )
| ( unordered_pair(sK0,sK1) = singleton(sK0) ) ),
inference(superposition,[status(thm)],[c_568,c_53]) ).
tcf(c_583,plain,
( ( sK3 = sK0 )
| ( unordered_pair(sK0,sK1) = singleton(sK0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_582,c_49]) ).
tcf(c_591,plain,
( member(unordered_pair(sK0,sK3),unordered_pair(singleton(sK0),singleton(sK0)))
| ( sK3 = sK0 ) ),
inference(superposition,[status(thm)],[c_583,c_526]) ).
tcf(c_636,plain,
( ( sK3 = sK0 )
| ( unordered_pair(sK0,sK3) = singleton(sK0) ) ),
inference(superposition,[status(thm)],[c_591,c_53]) ).
tcf(c_646,plain,
( member(sK3,singleton(sK0))
| ( sK3 = sK0 ) ),
inference(superposition,[status(thm)],[c_636,c_52]) ).
tcf(c_662,plain,
sK3 = sK0,
inference(forward_subsumption_resolution,[status(thm)],[c_646,c_55]) ).
tcf(c_667,plain,
( ( unordered_pair(sK3,sK1) = singleton(sK3) )
| ( unordered_pair(sK3,sK1) = unordered_pair(sK3,sK3) ) ),
inference(demodulation,[status(thm)],[c_543,c_662]) ).
tcf(c_700,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( unordered_pair(sK3,sK1) = singleton(sK3) )
| ~ member(X0,unordered_pair(sK3,sK1)) ),
inference(superposition,[status(thm)],[c_667,c_53]) ).
tcf(c_749,plain,
( ( sK1 = sK3 )
| ( unordered_pair(sK3,sK1) = singleton(sK3) ) ),
inference(superposition,[status(thm)],[c_52,c_700]) ).
tcf(c_750,plain,
unordered_pair(sK3,sK1) = singleton(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_749,c_49]) ).
tcf(c_763,plain,
member(sK1,singleton(sK3)),
inference(superposition,[status(thm)],[c_750,c_52]) ).
tcf(c_769,plain,
sK1 = sK3,
inference(superposition,[status(thm)],[c_763,c_55]) ).
tcf(c_770,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_769,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET018+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 09:10:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.03/0.33 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 3.50/1.06 % SZS status Started for theBenchmark.p
% 3.50/1.06 % SZS status Theorem for theBenchmark.p
% 3.50/1.06
% 3.50/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.50/1.06
% 3.50/1.06 % ------ iProver source info
% 3.50/1.06
% 3.50/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 3.50/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.50/1.06 % git: non_committed_changes: false
% 3.50/1.06
% 3.50/1.06 % ------ Parsing...
% 3.50/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.50/1.06
% 3.50/1.06 % ------ 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 %
% 3.50/1.06
% 3.50/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.50/1.06
% 3.50/1.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.50/1.06 % ------ Proving...
% 3.50/1.06 % ------ Problem Properties
% 3.50/1.06
% 3.50/1.06 %
% 3.50/1.06 % clauses 8
% 3.50/1.06 % conjectures 1
% 3.50/1.06 % EPR 1
% 3.50/1.06 % Horn 7
% 3.50/1.06 % unary 4
% 3.50/1.06 % binary 3
% 3.50/1.06 % lits 13
% 3.50/1.06 % lits eq 4
% 3.50/1.06 % fd_pure 0
% 3.50/1.06 % fd_pseudo 0
% 3.50/1.06 % fd_cond 0
% 3.50/1.06 % fd_pseudo_cond 2
% 3.50/1.06 % AC symbols 0
% 3.50/1.06
% 3.50/1.06 % ------ Schedule dynamic 5 is on
% 3.50/1.06
% 3.50/1.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.50/1.06
% 3.50/1.06
% 3.50/1.06 % ------
% 3.50/1.06 % Current options:
% 3.50/1.06 % ------
% 3.50/1.06
% 3.50/1.06
% 3.50/1.06 %
% 3.50/1.06
% 3.50/1.06 % ------ Proving...
% 3.50/1.06 %
% 3.50/1.06
% 3.50/1.06 % SZS status Theorem for theBenchmark.p
% 3.50/1.06
% 3.50/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.50/1.06
% 3.50/1.06
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