%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 02:46:36 PM UTC 2026
% Result : Theorem 2.06s 1.06s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 22 unt; 4 def)
% Number of atoms : 64 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 42 ( 20 ~; 14 |; 7 &)
% ( 1 <=>; 0 =>; 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 : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 34 !; 2 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(f44,conjecture,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_member_of_ordered_pair) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0,X1] : ~ member(singleton(X0),ordered_pair(X0,X1)),
inference(ennf_transformation,[],[f45]) ).
fof(f66,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(f67,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,[],[f66]) ).
fof(f103,plain,
~ member(singleton(sK6),ordered_pair(sK6,sK7)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f60]) ).
fof(f114,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f115,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f117,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f191,plain,
~ member(singleton(sK6),ordered_pair(sK6,sK7)),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f117,f116,f116]) ).
fof(f229,plain,
~ member(unordered_pair(sK6,sK6),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))),
inference(definition_unfolding,[],[f191,f116,f192]) ).
fof(f232,plain,
! [X2,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f114]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f115]) ).
tcf(c_128,negated_conjecture,
~ member(unordered_pair(sK6,sK6),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))),
inference(cnf_transformation,[],[f229]) ).
tcf(c_1552,definition,
iPr_def_10 = unordered_pair(sK6,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1553,definition,
iPr_def_11 = unordered_pair(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1554,definition,
iPr_def_12 = unordered_pair(sK6,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1555,definition,
iPr_def_13 = unordered_pair(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1556,negated_conjecture,
~ member(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_128,c_1553,c_1554,c_1555,c_1552]) ).
tcf(c_2376,plain,
member(iPr_def_10,universal_class),
inference(superposition,[status(thm)],[c_1552,c_60]) ).
tcf(c_2514,plain,
( member(iPr_def_10,iPr_def_13)
| ~ member(iPr_def_10,universal_class) ),
inference(superposition,[status(thm)],[c_1555,c_56]) ).
tcf(c_2515,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2514,c_1556,c_2376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Thu Sep 24 09:48:05 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 0.04/0.33
% 0.04/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.33
% 0.04/0.33 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 2.06/1.06 % SZS status Started for theBenchmark.p
% 2.06/1.06 % SZS status Theorem for theBenchmark.p
% 2.06/1.06
% 2.06/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.06/1.06
% 2.06/1.06 % ------ iProver source info
% 2.06/1.06
% 2.06/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 2.06/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.06/1.06 % git: non_committed_changes: false
% 2.06/1.06
% 2.06/1.06 % ------ Parsing...
% 2.06/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.06/1.06
% 2.06/1.06 % ------ 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: 4 0s sf_e pe_s pe_e %
% 2.06/1.06
% 2.06/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.06/1.06
% 2.06/1.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.06/1.06 % ------ Proving...
% 2.06/1.06 % ------ Problem Properties
% 2.06/1.06
% 2.06/1.06 %
% 2.06/1.06 % clauses 79
% 2.06/1.06 % conjectures 1
% 2.06/1.06 % EPR 8
% 2.06/1.06 % Horn 71
% 2.06/1.06 % unary 19
% 2.06/1.06 % binary 39
% 2.06/1.06 % lits 161
% 2.06/1.06 % lits eq 18
% 2.06/1.06 % fd_pure 0
% 2.06/1.06 % fd_pseudo 0
% 2.06/1.06 % fd_cond 4
% 2.06/1.06 % fd_pseudo_cond 3
% 2.06/1.06 % AC symbols 0
% 2.06/1.06
% 2.06/1.06 % ------ Schedule dynamic 5 is on
% 2.06/1.06
% 2.06/1.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.06/1.06
% 2.06/1.06
% 2.06/1.06 % ------
% 2.06/1.06 % Current options:
% 2.06/1.06 % ------
% 2.06/1.06
% 2.06/1.06
% 2.06/1.06 %
% 2.06/1.06
% 2.06/1.06 % ------ Proving...
% 2.06/1.06 %
% 2.06/1.06
% 2.06/1.06 % SZS status Theorem for theBenchmark.p
% 2.06/1.06
% 2.06/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.06/1.06
% 2.06/1.06
%------------------------------------------------------------------------------