%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET103+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 : n011.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 4.28s 16.33s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 24 unt; 6 def)
% Number of atoms : 118 ( 48 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 27 ~; 26 |; 15 &)
% ( 1 <=>; 1 =>; 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 : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 40 !; 4 ?; 9 :)
% 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(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(f41,axiom,
! [X0] :
( X0 != null_class
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(f44,conjecture,
! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_1_of_ordered_pair) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f57,plain,
! [X0] :
( null_class = X0
| ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f60,plain,
? [X0,X1] :
( ~ member(X1,universal_class)
& ordered_pair(X0,X1) != unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
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(f101,plain,
! [X0] :
( null_class = X0
| ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f57]) ).
fof(f103,plain,
( ~ member(sK7,universal_class)
& ordered_pair(sK6,sK7) != unordered_pair(singleton(sK6),unordered_pair(sK6,null_class)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f60]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) ),
inference(cnf_transformation,[],[f67]) ).
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(f186,plain,
! [X0] :
( null_class = X0
| member(sK4(X0),X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f191,plain,
~ member(sK7,universal_class),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
ordered_pair(sK6,sK7) != unordered_pair(singleton(sK6),unordered_pair(sK6,null_class)),
inference(cnf_transformation,[],[f103]) ).
fof(f193,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(f230,plain,
unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))) != unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,null_class)),
inference(definition_unfolding,[],[f192,f193,f116]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_124,plain,
! [X0: $i] :
( member(sK4(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_128,negated_conjecture,
unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))) != unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,null_class)),
inference(cnf_transformation,[],[f230]) ).
tcf(c_129,negated_conjecture,
~ member(sK7,universal_class),
inference(cnf_transformation,[],[f191]) ).
tcf(c_1557,definition,
iPr_def_10 = unordered_pair(sK6,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1558,definition,
iPr_def_11 = unordered_pair(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1559,definition,
iPr_def_12 = unordered_pair(sK6,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1560,definition,
iPr_def_13 = unordered_pair(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1561,definition,
iPr_def_14 = unordered_pair(sK6,null_class),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1562,definition,
iPr_def_15 = unordered_pair(iPr_def_10,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_1563,negated_conjecture,
~ member(sK7,universal_class),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_1564,negated_conjecture,
iPr_def_13 != iPr_def_15,
inference(demodulation,[status(thm)],[c_128,c_1561,c_1562,c_1558,c_1559,c_1557,c_1560]) ).
tcf(c_2540,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1558,c_58]) ).
tcf(c_2623,plain,
( member(sK4(iPr_def_11),universal_class)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_124,c_2540]) ).
tcf(c_3557,plain,
! [X0: $i] :
( ( X0 = sK7 )
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1558,c_59]) ).
tcf(c_4104,plain,
( ( null_class = iPr_def_11 )
| ( sK4(iPr_def_11) = sK7 ) ),
inference(superposition,[status(thm)],[c_124,c_3557]) ).
tcf(c_4679,plain,
( member(sK7,universal_class)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_4104,c_2623]) ).
tcf(c_4680,plain,
null_class = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_4679,c_1563]) ).
tcf(c_4707,plain,
unordered_pair(sK6,iPr_def_11) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1561,c_4680]) ).
tcf(c_4710,plain,
iPr_def_12 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_4707,c_1559]) ).
tcf(c_4719,plain,
unordered_pair(iPr_def_10,iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_1562,c_4710]) ).
tcf(c_4721,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_4719,c_1560]) ).
tcf(c_4722,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4721,c_1564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET103+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.41 % CPULimit : 300
% 0.07/15.41 % WCLimit : 300
% 0.07/15.41 % DateTime : Thu Sep 24 09:49:05 UTC 2026
% 0.07/15.42 % CPUTime :
% 0.07/15.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/15.45 Running first-order theorem proving
% 0.07/15.46 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
% 0.07/15.47
% 0.07/15.47 % ======== iProver multi-core TPTP/SMT =========
% 0.07/15.47
% 0.07/15.47 % Detected problem language: tptp
% 0.07/15.48 % Proving...
% 4.28/16.33 % SZS status Started for theBenchmark.p
% 4.28/16.33 % SZS status Theorem for theBenchmark.p
% 4.28/16.33
% 4.28/16.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.28/16.33
% 4.28/16.33 % ------ iProver source info
% 4.28/16.33
% 4.28/16.33 % git: date: 2026-07-19 20:42:38 +0200
% 4.28/16.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.28/16.33 % git: non_committed_changes: false
% 4.28/16.33
% 4.28/16.33 % ------ Parsing...
% 4.28/16.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.28/16.33
% 4.28/16.33 % ------ 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 %
% 4.28/16.33
% 4.28/16.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.28/16.33
% 4.28/16.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.28/16.33 % ------ Proving...
% 4.28/16.33 % ------ Problem Properties
% 4.28/16.33
% 4.28/16.33 %
% 4.28/16.33 % clauses 82
% 4.28/16.33 % conjectures 2
% 4.28/16.33 % EPR 9
% 4.28/16.33 % Horn 74
% 4.28/16.33 % unary 22
% 4.28/16.33 % binary 39
% 4.28/16.33 % lits 164
% 4.28/16.33 % lits eq 21
% 4.28/16.33 % fd_pure 0
% 4.28/16.33 % fd_pseudo 0
% 4.28/16.33 % fd_cond 4
% 4.28/16.33 % fd_pseudo_cond 3
% 4.28/16.33 % AC symbols 0
% 4.28/16.33
% 4.28/16.33 % ------ Schedule dynamic 5 is on
% 4.28/16.33
% 4.28/16.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.28/16.33
% 4.28/16.33
% 4.28/16.33 % ------
% 4.28/16.33 % Current options:
% 4.28/16.33 % ------
% 4.28/16.33
% 4.28/16.33
% 4.28/16.33 %
% 4.28/16.33
% 4.28/16.33 % ------ Proving...
% 4.28/16.33 %
% 4.28/16.33
% 4.28/16.33 % SZS status Theorem for theBenchmark.p
% 4.28/16.33
% 4.28/16.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.28/16.33
% 4.28/16.33
%------------------------------------------------------------------------------