%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 02:46:37 PM UTC 2026
% Result : Theorem 1.04s 1.29s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 20 unt; 4 def)
% Number of atoms : 108 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 100 ( 47 ~; 35 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 37 !; 11 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(f44,conjecture,
! [X0] :
? [X1,X2] :
( ( X2 = X0
& X1 = X0
& ~ ? [X3,X4] :
( X0 = ordered_pair(X3,X4)
& member(X4,universal_class)
& member(X3,universal_class) ) )
| ( X0 = ordered_pair(X1,X2)
& member(X2,universal_class)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_first_and_second) ).
fof(f45,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ( X2 = X0
& X1 = X0
& ~ ? [X3,X4] :
( X0 = ordered_pair(X3,X4)
& member(X4,universal_class)
& member(X3,universal_class) ) )
| ( X0 = ordered_pair(X1,X2)
& member(X2,universal_class)
& member(X1,universal_class) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0] :
! [X1,X2] :
( ( X0 != X2
| X0 != X1
| ? [X3,X4] :
( X0 = ordered_pair(X3,X4)
& member(X4,universal_class)
& member(X3,universal_class) ) )
& ( ordered_pair(X1,X2) != X0
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f103,plain,
! [X1,X2] :
( ( sK6 != X2
| sK6 != X1
| ( sK6 = ordered_pair(sK7,sK8)
& member(sK8,universal_class)
& member(sK7,universal_class) ) )
& ( ordered_pair(X1,X2) != sK6
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X3,sK7),skolemize(X4,sK8)],[f60]) ).
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,
! [X2,X1] :
( sK6 != X2
| sK6 != X1
| sK6 = ordered_pair(sK7,sK8) ),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
! [X2,X1] :
( sK6 != X2
| sK6 != X1
| member(sK8,universal_class) ),
inference(cnf_transformation,[],[f103]) ).
fof(f193,plain,
! [X2,X1] :
( sK6 != X2
| sK6 != X1
| member(sK7,universal_class) ),
inference(cnf_transformation,[],[f103]) ).
fof(f194,plain,
! [X2,X1] :
( ordered_pair(X1,X2) != sK6
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f103]) ).
fof(f195,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(f232,plain,
! [X2,X1] :
( sK6 != unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f194,f195]) ).
fof(f233,plain,
! [X2,X1] :
( sK6 != X2
| sK6 != X1
| sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))) ),
inference(definition_unfolding,[],[f191,f195]) ).
fof(f240,plain,
! [X2] :
( sK6 != X2
| member(sK7,universal_class) ),
inference(equality_resolution,[],[f193]) ).
fof(f241,plain,
member(sK7,universal_class),
inference(equality_resolution,[],[f240]) ).
fof(f242,plain,
! [X2] :
( sK6 != X2
| member(sK8,universal_class) ),
inference(equality_resolution,[],[f192]) ).
fof(f243,plain,
member(sK8,universal_class),
inference(equality_resolution,[],[f242]) ).
fof(f244,plain,
! [X2] :
( sK6 != X2
| sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))) ),
inference(equality_resolution,[],[f233]) ).
fof(f245,plain,
sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))),
inference(equality_resolution,[],[f244]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) != sK6 ) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_129,negated_conjecture,
member(sK7,universal_class),
inference(cnf_transformation,[],[f241]) ).
tcf(c_130,negated_conjecture,
member(sK8,universal_class),
inference(cnf_transformation,[],[f243]) ).
tcf(c_131,negated_conjecture,
unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))) = sK6,
inference(cnf_transformation,[],[f245]) ).
tcf(c_1588,definition,
iPr_def_10 = unordered_pair(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1589,definition,
iPr_def_11 = unordered_pair(sK8,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1590,definition,
iPr_def_12 = unordered_pair(sK7,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1591,definition,
iPr_def_13 = unordered_pair(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1592,negated_conjecture,
iPr_def_13 = sK6,
inference(demodulation,[status(thm)],[c_131,c_1589,c_1590,c_1588,c_1591]) ).
tcf(c_1593,negated_conjecture,
member(sK8,universal_class),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_1594,negated_conjecture,
member(sK7,universal_class),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_1595,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) != sK6 ) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_2433,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_1595,c_1592]) ).
tcf(c_2437,plain,
! [X0: $i] :
( ~ member(sK7,universal_class)
| ~ member(X0,universal_class)
| ( unordered_pair(iPr_def_10,unordered_pair(sK7,unordered_pair(X0,X0))) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1588,c_2433]) ).
tcf(c_2442,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ( unordered_pair(iPr_def_10,unordered_pair(sK7,unordered_pair(X0,X0))) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2437,c_1594]) ).
tcf(c_2472,plain,
( ~ member(sK8,universal_class)
| ( unordered_pair(iPr_def_10,unordered_pair(sK7,iPr_def_11)) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1589,c_2442]) ).
tcf(c_2473,plain,
~ member(sK8,universal_class),
inference(ground_joinability,[status(thm)],[c_2472,c_1590,c_1591]) ).
tcf(c_2474,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2473,c_1593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:53:39 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.04/1.29 % SZS status Started for theBenchmark.p
% 1.04/1.29 % SZS status Theorem for theBenchmark.p
% 1.04/1.29
% 1.04/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.04/1.29
% 1.04/1.29 % ------ iProver source info
% 1.04/1.29
% 1.04/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.04/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.04/1.29 % git: non_committed_changes: false
% 1.04/1.29
% 1.04/1.29 % ------ Parsing...
% 1.04/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.04/1.29
% 1.04/1.29 % ------ 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 %
% 1.04/1.29
% 1.04/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.04/1.29
% 1.04/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.04/1.29 % ------ Proving...
% 1.04/1.29 % ------ Problem Properties
% 1.04/1.29
% 1.04/1.29 %
% 1.04/1.29 % clauses 82
% 1.04/1.29 % conjectures 4
% 1.04/1.29 % EPR 10
% 1.04/1.29 % Horn 74
% 1.04/1.29 % unary 21
% 1.04/1.29 % binary 39
% 1.04/1.29 % lits 166
% 1.04/1.29 % lits eq 20
% 1.04/1.29 % fd_pure 0
% 1.04/1.29 % fd_pseudo 0
% 1.04/1.29 % fd_cond 4
% 1.04/1.29 % fd_pseudo_cond 3
% 1.04/1.29 % AC symbols 0
% 1.04/1.29
% 1.04/1.29 % ------ Schedule dynamic 5 is on
% 1.04/1.29
% 1.04/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.04/1.29
% 1.04/1.29
% 1.04/1.29 % ------
% 1.04/1.29 % Current options:
% 1.04/1.29 % ------
% 1.04/1.29
% 1.04/1.29
% 1.04/1.29 %
% 1.04/1.29
% 1.04/1.29 % ------ Proving...
% 1.04/1.29 %
% 1.04/1.29
% 1.04/1.29 % SZS status Theorem for theBenchmark.p
% 1.04/1.29
% 1.04/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.04/1.29
% 1.04/1.29
%------------------------------------------------------------------------------