%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET084+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 : n001.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 02:46:30 PM UTC 2026
% Result : Theorem 2.81s 6.29s
% Output : CNFRefutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 18 unt; 2 def)
% Number of atoms : 78 ( 39 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 60 ( 23 ~; 19 |; 15 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 29 !; 4 ?; 6 :)
% 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,conjecture,
! [X0,X1] :
( ( member(X1,universal_class)
& singleton(X0) = singleton(X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element2) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( ( member(X1,universal_class)
& singleton(X0) = singleton(X1) )
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0,X1] :
( member(X1,universal_class)
& singleton(X0) = singleton(X1)
& X0 != X1 ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
? [X0,X1] :
( member(X1,universal_class)
& singleton(X0) = singleton(X1)
& X0 != X1 ),
inference(flattening,[],[f60]) ).
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(nnf_transformation,[],[f4]) ).
fof(f68,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,[],[f67]) ).
fof(f104,plain,
( member(sK7,universal_class)
& singleton(sK6) = singleton(sK7)
& sK6 != sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f61]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f115,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f192,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f104]) ).
fof(f193,plain,
singleton(sK6) = singleton(sK7),
inference(cnf_transformation,[],[f104]) ).
fof(f194,plain,
sK6 != sK7,
inference(cnf_transformation,[],[f104]) ).
fof(f232,plain,
unordered_pair(sK6,sK6) = unordered_pair(sK7,sK7),
inference(definition_unfolding,[],[f193,f117,f117]) ).
fof(f235,plain,
! [X2,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f115]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_128,negated_conjecture,
sK6 != sK7,
inference(cnf_transformation,[],[f194]) ).
tcf(c_129,negated_conjecture,
unordered_pair(sK6,sK6) = unordered_pair(sK7,sK7),
inference(cnf_transformation,[],[f232]) ).
tcf(c_130,negated_conjecture,
member(sK7,universal_class),
inference(cnf_transformation,[],[f192]) ).
tcf(c_1562,definition,
iPr_def_10 = unordered_pair(sK6,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1563,definition,
iPr_def_11 = unordered_pair(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1564,negated_conjecture,
member(sK7,universal_class),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_1565,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_129,c_1563,c_1562]) ).
tcf(c_1566,negated_conjecture,
sK6 != sK7,
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_2385,plain,
unordered_pair(sK7,sK7) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1563,c_1565]) ).
tcf(c_2486,plain,
( member(sK7,iPr_def_10)
| ~ member(sK7,universal_class) ),
inference(superposition,[status(thm)],[c_2385,c_56]) ).
tcf(c_2487,plain,
member(sK7,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2486,c_1564]) ).
tcf(c_3201,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1562,c_59]) ).
tcf(c_4043,plain,
sK6 = sK7,
inference(superposition,[status(thm)],[c_2487,c_3201]) ).
tcf(c_4045,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4043,c_1566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET084+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n001.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 09:46:28 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 2.81/6.29 % SZS status Started for theBenchmark.p
% 2.81/6.29 % SZS status Theorem for theBenchmark.p
% 2.81/6.29
% 2.81/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.81/6.29
% 2.81/6.29 % ------ iProver source info
% 2.81/6.29
% 2.81/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.81/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.81/6.29 % git: non_committed_changes: false
% 2.81/6.29
% 2.81/6.29 % ------ Parsing...
% 2.81/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.81/6.29
% 2.81/6.29 % ------ 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 %
% 2.81/6.29
% 2.81/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.81/6.29
% 2.81/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.81/6.29 % ------ Proving...
% 2.81/6.29 % ------ Problem Properties
% 2.81/6.29
% 2.81/6.29 %
% 2.81/6.29 % clauses 79
% 2.81/6.29 % conjectures 3
% 2.81/6.29 % EPR 10
% 2.81/6.29 % Horn 71
% 2.81/6.29 % unary 19
% 2.81/6.29 % binary 39
% 2.81/6.29 % lits 161
% 2.81/6.29 % lits eq 18
% 2.81/6.29 % fd_pure 0
% 2.81/6.29 % fd_pseudo 0
% 2.81/6.29 % fd_cond 4
% 2.81/6.29 % fd_pseudo_cond 3
% 2.81/6.29 % AC symbols 0
% 2.81/6.29
% 2.81/6.29 % ------ Schedule dynamic 5 is on
% 2.81/6.29
% 2.81/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.81/6.29
% 2.81/6.29
% 2.81/6.29 % ------
% 2.81/6.29 % Current options:
% 2.81/6.29 % ------
% 2.81/6.29
% 2.81/6.29
% 2.81/6.29 %
% 2.81/6.29
% 2.81/6.29 % ------ Proving...
% 2.81/6.29 %
% 2.81/6.29
% 2.81/6.29 % SZS status Theorem for theBenchmark.p
% 2.81/6.29
% 2.81/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.81/6.29
% 2.81/6.29
%------------------------------------------------------------------------------