%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU144+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 02:55:34 PM UTC 2026
% Result : Theorem 5.94s 1.74s
% Output : CNFRefutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 11 unt; 1 def)
% Number of atoms : 206 ( 78 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 226 ( 85 ~; 94 |; 37 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 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; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 102 ( 0 sgn 91 !; 11 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f11,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f29,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f60,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f76,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f81,plain,
? [X0,X1] :
( subset(singleton(X0),X1)
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f106,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f107,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f107]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| sK2(X0,X1,X2) = X1
| sK2(X0,X1,X2) = X0 )
& ( ~ in(sK2(X0,X1,X2),X2)
| ( sK2(X0,X1,X2) != X1
& sK2(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f114]) ).
fof(f120,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f121,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK4(X0,X1),X0)
& ~ in(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f121]) ).
fof(f132,plain,
? [X0,X1] :
( ( subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ subset(singleton(X0),X1)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f133,plain,
( ( subset(singleton(sK7),sK8)
| in(sK7,sK8) )
& ( ~ subset(singleton(sK7),sK8)
| ~ in(sK7,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f132]) ).
fof(f151,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f108]) ).
fof(f158,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f169,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f170,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f171,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f194,plain,
( subset(singleton(sK7),sK8)
| in(sK7,sK8) ),
inference(cnf_transformation,[],[f133]) ).
fof(f195,plain,
( ~ subset(singleton(sK7),sK8)
| ~ in(sK7,sK8) ),
inference(cnf_transformation,[],[f133]) ).
fof(f231,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f60]) ).
fof(f243,plain,
! [X3,X0,X1] :
( unordered_pair(X0,X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(definition_unfolding,[],[f151,f231]) ).
fof(f254,plain,
( ~ subset(unordered_pair(sK7,sK7),sK8)
| ~ in(sK7,sK8) ),
inference(definition_unfolding,[],[f195,f231]) ).
fof(f255,plain,
( subset(unordered_pair(sK7,sK7),sK8)
| in(sK7,sK8) ),
inference(definition_unfolding,[],[f194,f231]) ).
fof(f267,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f243]) ).
fof(f271,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f158]) ).
fof(f272,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f271]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f272]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_100,negated_conjecture,
( ~ in(sK7,sK8)
| ~ subset(unordered_pair(sK7,sK7),sK8) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_101,negated_conjecture,
( in(sK7,sK8)
| subset(unordered_pair(sK7,sK7),sK8) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_2076,definition,
iPr_def_10 = unordered_pair(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2077,negated_conjecture,
( subset(iPr_def_10,sK8)
| in(sK7,sK8) ),
inference(demodulation,[status(thm)],[c_101,c_2076]) ).
tcf(c_2078,negated_conjecture,
( ~ subset(iPr_def_10,sK8)
| ~ in(sK7,sK8) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_3459,plain,
in(sK7,iPr_def_10),
inference(superposition,[status(thm)],[c_2076,c_67]) ).
tcf(c_4243,plain,
! [X0: $i] :
( in(sK7,X0)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_3459,c_77]) ).
tcf(c_4344,plain,
in(sK7,sK8),
inference(backward_subsumption_resolution,[status(thm)],[c_2077,c_4243]) ).
tcf(c_5301,negated_conjecture,
in(sK7,sK8),
inference(global_subsumption_just,[status(thm)],[c_2077,c_4344]) ).
tcf(c_5414,negated_conjecture,
~ subset(iPr_def_10,sK8),
inference(global_subsumption_just,[status(thm)],[c_2078,c_2078,c_4344]) ).
tcf(c_6886,plain,
! [X0: $i] :
( ( X0 = sK7 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2076,c_60]) ).
tcf(c_6988,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ( sK4(iPr_def_10,X0) = sK7 ) ),
inference(superposition,[status(thm)],[c_76,c_6886]) ).
tcf(c_7180,plain,
sK4(iPr_def_10,sK8) = sK7,
inference(superposition,[status(thm)],[c_6988,c_5414]) ).
tcf(c_7182,plain,
( subset(iPr_def_10,sK8)
| ~ in(sK7,sK8) ),
inference(superposition,[status(thm)],[c_7180,c_75]) ).
tcf(c_7185,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7182,c_5414,c_5301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU144+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:56:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 5.94/1.74 % SZS status Started for theBenchmark.p
% 5.94/1.74 % SZS status Theorem for theBenchmark.p
% 5.94/1.74
% 5.94/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.94/1.74
% 5.94/1.74 % ------ iProver source info
% 5.94/1.74
% 5.94/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 5.94/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.94/1.74 % git: non_committed_changes: false
% 5.94/1.74
% 5.94/1.74 % ------ Parsing...
% 5.94/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.94/1.74
% 5.94/1.74 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 5.94/1.74
% 5.94/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.94/1.74
% 5.94/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.94/1.74 % ------ Proving...
% 5.94/1.74 % ------ Problem Properties
% 5.94/1.74
% 5.94/1.74 %
% 5.94/1.74 % clauses 86
% 5.94/1.74 % conjectures 2
% 5.94/1.74 % EPR 23
% 5.94/1.74 % Horn 67
% 5.94/1.74 % unary 23
% 5.94/1.74 % binary 34
% 5.94/1.74 % lits 182
% 5.94/1.74 % lits eq 51
% 5.94/1.74 % fd_pure 0
% 5.94/1.74 % fd_pseudo 0
% 5.94/1.74 % fd_cond 3
% 5.94/1.74 % fd_pseudo_cond 19
% 5.94/1.74 % AC symbols 0
% 5.94/1.74
% 5.94/1.74 % ------ Schedule dynamic 5 is on
% 5.94/1.74
% 5.94/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.94/1.74
% 5.94/1.74
% 5.94/1.74 % ------
% 5.94/1.74 % Current options:
% 5.94/1.74 % ------
% 5.94/1.74
% 5.94/1.74
% 5.94/1.74 %
% 5.94/1.74
% 5.94/1.74 % ------ Proving...
% 5.94/1.74 %
% 5.94/1.74
% 5.94/1.74 % SZS status Theorem for theBenchmark.p
% 5.94/1.74
% 5.94/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.94/1.74
% 5.94/1.74
%------------------------------------------------------------------------------