%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 02:46:32 PM UTC 2026
% Result : Theorem 4.12s 1.28s
% Output : CNFRefutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 24 unt; 2 def)
% Number of atoms : 173 ( 67 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 104 ( 40 ~; 44 |; 15 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 51 !; 4 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f44,axiom,
! [X0] :
( member(X0,universal_class)
=> member(member_of(singleton(X0)),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_singleton_universal) ).
fof(f45,axiom,
! [X0] :
( member(X0,universal_class)
=> singleton(member_of(singleton(X0))) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_singleton_singleton) ).
fof(f47,axiom,
! [X0] :
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_self) ).
fof(f48,conjecture,
! [X0,X1] :
( ( X0 = singleton(X1)
& member(X1,universal_class) )
=> member_of(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_singleton) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( ( X0 = singleton(X1)
& member(X1,universal_class) )
=> member_of(X0) = X1 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f64,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(member_of(singleton(X0)),universal_class) ),
inference(ennf_transformation,[],[f44]) ).
fof(f65,plain,
! [X0] :
( ~ member(X0,universal_class)
| singleton(member_of(singleton(X0))) = singleton(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f66,plain,
? [X0,X1] :
( X0 = singleton(X1)
& member(X1,universal_class)
& member_of(X0) != X1 ),
inference(ennf_transformation,[],[f49]) ).
fof(f67,plain,
? [X0,X1] :
( X0 = singleton(X1)
& member(X1,universal_class)
& member_of(X0) != X1 ),
inference(flattening,[],[f66]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) )
& ( ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) )
& ( ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f73]) ).
fof(f110,plain,
( sK6 = singleton(sK7)
& member(sK7,universal_class)
& sK7 != member_of(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f67]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f120,plain,
! [X2,X0,X1] :
( X0 != X2
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f123,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f198,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(member_of(singleton(X0)),universal_class) ),
inference(cnf_transformation,[],[f64]) ).
fof(f199,plain,
! [X0] :
( ~ member(X0,universal_class)
| singleton(X0) = singleton(member_of(singleton(X0))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f201,plain,
! [X0] :
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f202,plain,
sK6 = singleton(sK7),
inference(cnf_transformation,[],[f110]) ).
fof(f203,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f110]) ).
fof(f204,plain,
sK7 != member_of(sK6),
inference(cnf_transformation,[],[f110]) ).
fof(f242,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(member_of(unordered_pair(X0,X0)),universal_class) ),
inference(definition_unfolding,[],[f198,f123]) ).
fof(f243,plain,
! [X0] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X0) = unordered_pair(member_of(unordered_pair(X0,X0)),member_of(unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f199,f123,f123,f123]) ).
fof(f244,plain,
! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ),
inference(definition_unfolding,[],[f201,f123]) ).
fof(f245,plain,
sK6 = unordered_pair(sK7,sK7),
inference(definition_unfolding,[],[f202,f123]) ).
fof(f248,plain,
! [X2,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f121]) ).
fof(f249,plain,
! [X2,X1] :
( ~ member(X2,universal_class)
| member(X2,unordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f120]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_128,plain,
! [X0: $i] :
( member(member_of(unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_129,plain,
! [X0: $i] :
( ( unordered_pair(member_of(unordered_pair(X0,X0)),member_of(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_131,plain,
! [X0: $i] :
( ( member_of(X0) = X0 )
| ( unordered_pair(member_of(X0),member_of(X0)) = X0 ) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_132,negated_conjecture,
member_of(sK6) != sK7,
inference(cnf_transformation,[],[f204]) ).
tcf(c_133,negated_conjecture,
member(sK7,universal_class),
inference(cnf_transformation,[],[f203]) ).
tcf(c_134,negated_conjecture,
unordered_pair(sK7,sK7) = sK6,
inference(cnf_transformation,[],[f245]) ).
tcf(c_1636,definition,
iPr_def_10 = unordered_pair(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1637,definition,
iPr_def_11 = member_of(sK6),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1638,negated_conjecture,
iPr_def_10 = sK6,
inference(demodulation,[status(thm)],[c_134,c_1636]) ).
tcf(c_1639,negated_conjecture,
member(sK7,universal_class),
inference(demodulation,[status(thm)],[c_133]) ).
tcf(c_1640,negated_conjecture,
iPr_def_11 != sK7,
inference(demodulation,[status(thm)],[c_132,c_1637]) ).
tcf(c_2501,plain,
member_of(iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1637,c_1638]) ).
tcf(c_2600,plain,
( member(sK7,iPr_def_10)
| ~ member(sK7,universal_class) ),
inference(superposition,[status(thm)],[c_1636,c_56]) ).
tcf(c_2601,plain,
member(sK7,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2600,c_1639]) ).
tcf(c_2774,plain,
( member(member_of(iPr_def_10),universal_class)
| ~ member(sK7,universal_class) ),
inference(superposition,[status(thm)],[c_1636,c_128]) ).
tcf(c_2775,plain,
( member(iPr_def_11,universal_class)
| ~ member(sK7,universal_class) ),
inference(light_normalisation,[status(thm)],[c_2774,c_2501]) ).
tcf(c_2776,plain,
member(iPr_def_11,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_2775,c_1639]) ).
tcf(c_3312,plain,
( ( member_of(iPr_def_10) = iPr_def_10 )
| ( unordered_pair(iPr_def_11,iPr_def_11) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2501,c_131]) ).
tcf(c_3322,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( unordered_pair(iPr_def_11,iPr_def_11) = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_3312,c_2501]) ).
tcf(c_3447,plain,
( member(iPr_def_11,iPr_def_10)
| ( iPr_def_10 = iPr_def_11 )
| ~ member(iPr_def_11,universal_class) ),
inference(superposition,[status(thm)],[c_3322,c_57]) ).
tcf(c_3457,plain,
( member(iPr_def_11,iPr_def_10)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3447,c_2776]) ).
tcf(c_3765,plain,
! [X0: $i] :
( ( X0 = sK7 )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1636,c_59]) ).
tcf(c_4367,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( sK7 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_3457,c_3765]) ).
tcf(c_4572,plain,
iPr_def_10 = iPr_def_11,
inference(superposition,[status(thm)],[c_4367,c_1640]) ).
tcf(c_4578,plain,
member_of(iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2501,c_4572]) ).
tcf(c_4579,plain,
sK7 != iPr_def_10,
inference(demodulation,[status(thm)],[c_1640,c_4572]) ).
tcf(c_4695,plain,
unordered_pair(member_of(unordered_pair(sK7,sK7)),member_of(unordered_pair(sK7,sK7))) = unordered_pair(sK7,sK7),
inference(superposition,[status(thm)],[c_1639,c_129]) ).
tcf(c_4706,plain,
unordered_pair(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_4695,c_1636,c_4578]) ).
tcf(c_4851,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4706,c_59]) ).
tcf(c_4947,plain,
sK7 = iPr_def_10,
inference(superposition,[status(thm)],[c_2601,c_4851]) ).
tcf(c_4950,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4947,c_4579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.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 09:42:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 4.12/1.28 % SZS status Started for theBenchmark.p
% 4.12/1.28 % SZS status Theorem for theBenchmark.p
% 4.12/1.28
% 4.12/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.12/1.28
% 4.12/1.28 % ------ iProver source info
% 4.12/1.28
% 4.12/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.12/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.12/1.28 % git: non_committed_changes: false
% 4.12/1.28
% 4.12/1.28 % ------ Parsing...
% 4.12/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.12/1.28
% 4.12/1.28 % ------ 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: 4 0s sf_e pe_s pe_e %
% 4.12/1.28
% 4.12/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.12/1.28
% 4.12/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.12/1.28 % ------ Proving...
% 4.12/1.28 % ------ Problem Properties
% 4.12/1.28
% 4.12/1.28 %
% 4.12/1.28 % clauses 83
% 4.12/1.28 % conjectures 3
% 4.12/1.28 % EPR 10
% 4.12/1.28 % Horn 73
% 4.12/1.28 % unary 19
% 4.12/1.28 % binary 43
% 4.12/1.28 % lits 169
% 4.12/1.28 % lits eq 22
% 4.12/1.28 % fd_pure 0
% 4.12/1.28 % fd_pseudo 0
% 4.12/1.28 % fd_cond 4
% 4.12/1.28 % fd_pseudo_cond 3
% 4.12/1.28 % AC symbols 0
% 4.12/1.28
% 4.12/1.28 % ------ Schedule dynamic 5 is on
% 4.12/1.28
% 4.12/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.12/1.28
% 4.12/1.28
% 4.12/1.28 % ------
% 4.12/1.28 % Current options:
% 4.12/1.28 % ------
% 4.12/1.28
% 4.12/1.28
% 4.12/1.28 %
% 4.12/1.28
% 4.12/1.28 % ------ Proving...
% 4.12/1.28 %
% 4.12/1.28
% 4.12/1.28 % SZS status Theorem for theBenchmark.p
% 4.12/1.28
% 4.12/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.12/1.28
% 4.12/1.28
%------------------------------------------------------------------------------