%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU148+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 02:55:36 PM UTC 2026
% Result : Theorem 1.24s 1.29s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 20 unt; 2 def)
% Number of atoms : 273 ( 99 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 308 ( 115 ~; 122 |; 58 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 145 ( 0 sgn 133 !; 12 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f11,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f12,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f31,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f39,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f64,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f66,conjecture,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f67,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f82,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f90,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f39]) ).
fof(f107,plain,
? [X0,X1] :
( subset(singleton(X0),singleton(X1))
& X0 != X1 ),
inference(ennf_transformation,[],[f67]) ).
fof(f114,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(f115,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,[],[f114]) ).
fof(f116,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))],[f115]) ).
fof(f123,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,[],[f10]) ).
fof(f124,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,[],[f123]) ).
fof(f125,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,[],[f124]) ).
fof(f126,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(sK3(X0,X1,X2),X2)
| sK3(X0,X1,X2) = X1
| sK3(X0,X1,X2) = X0 )
& ( ~ in(sK3(X0,X1,X2),X2)
| ( sK3(X0,X1,X2) != X1
& sK3(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f125]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK4(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X0) )
& ( ~ in(sK4(X0,X1,X2),X2)
| ( ~ in(sK4(X0,X1,X2),X1)
& ~ in(sK4(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f129]) ).
fof(f131,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,[],[f82]) ).
fof(f132,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,[],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK5(X0,X1),X0)
& ~ in(sK5(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f132]) ).
fof(f143,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f154,plain,
( subset(singleton(sK13),singleton(sK14))
& sK13 != sK14 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f107]) ).
fof(f164,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f116]) ).
fof(f176,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f126]) ).
fof(f182,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f186,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f212,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f223,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f90]) ).
fof(f253,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f64]) ).
fof(f255,plain,
subset(singleton(sK13),singleton(sK14)),
inference(cnf_transformation,[],[f154]) ).
fof(f256,plain,
sK13 != sK14,
inference(cnf_transformation,[],[f154]) ).
fof(f267,plain,
! [X3,X0,X1] :
( unordered_pair(X0,X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(definition_unfolding,[],[f164,f253]) ).
fof(f278,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f212,f253]) ).
fof(f292,plain,
subset(unordered_pair(sK13,sK13),unordered_pair(sK14,sK14)),
inference(definition_unfolding,[],[f255,f253,f253]) ).
fof(f297,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f267]) ).
fof(f301,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f176]) ).
fof(f302,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f301]) ).
fof(f306,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f182]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f297]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f302]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_146,negated_conjecture,
sK13 != sK14,
inference(cnf_transformation,[],[f256]) ).
tcf(c_147,negated_conjecture,
subset(unordered_pair(sK13,sK13),unordered_pair(sK14,sK14)),
inference(cnf_transformation,[],[f292]) ).
tcf(c_2275,definition,
iPr_def_10 = unordered_pair(sK13,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2276,definition,
iPr_def_11 = unordered_pair(sK14,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2277,negated_conjecture,
subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_147,c_2276,c_2275]) ).
tcf(c_2278,negated_conjecture,
sK13 != sK14,
inference(demodulation,[status(thm)],[c_146]) ).
tcf(c_3782,plain,
in(sK13,iPr_def_10),
inference(superposition,[status(thm)],[c_2275,c_70]) ).
tcf(c_4142,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| ~ in(sK14,X0) ),
inference(superposition,[status(thm)],[c_2276,c_104]) ).
tcf(c_4249,plain,
set_union2(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_2277,c_116]) ).
tcf(c_4285,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4249,c_76]) ).
tcf(c_4308,plain,
in(sK13,iPr_def_11),
inference(superposition,[status(thm)],[c_3782,c_4285]) ).
tcf(c_4542,plain,
! [X0: $i] : subset(iPr_def_11,unordered_pair(sK14,X0)),
inference(superposition,[status(thm)],[c_70,c_4142]) ).
tcf(c_4627,plain,
! [X0: $i] :
( in(sK13,X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4308,c_81]) ).
tcf(c_4759,plain,
! [X0: $i] : in(sK13,unordered_pair(sK14,X0)),
inference(superposition,[status(thm)],[c_4542,c_4627]) ).
tcf(c_4969,plain,
sK13 = sK14,
inference(superposition,[status(thm)],[c_4759,c_60]) ).
tcf(c_4971,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4969,c_2278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU148+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 13:00:25 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 1.24/1.29 % SZS status Started for theBenchmark.p
% 1.24/1.29 % SZS status Theorem for theBenchmark.p
% 1.24/1.29
% 1.24/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.24/1.29
% 1.24/1.29 % ------ iProver source info
% 1.24/1.29
% 1.24/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.24/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.24/1.29 % git: non_committed_changes: false
% 1.24/1.29
% 1.24/1.29 % ------ Parsing...
% 1.24/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.24/1.29
% 1.24/1.29 % ------ 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 %
% 1.24/1.29
% 1.24/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.24/1.29
% 1.24/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.24/1.29 % ------ Proving...
% 1.24/1.29 % ------ Problem Properties
% 1.24/1.29
% 1.24/1.29 %
% 1.24/1.29 % clauses 96
% 1.24/1.29 % conjectures 2
% 1.24/1.29 % EPR 23
% 1.24/1.29 % Horn 75
% 1.24/1.29 % unary 27
% 1.24/1.29 % binary 36
% 1.24/1.29 % lits 202
% 1.24/1.29 % lits eq 58
% 1.24/1.29 % fd_pure 0
% 1.24/1.29 % fd_pseudo 0
% 1.24/1.29 % fd_cond 3
% 1.24/1.29 % fd_pseudo_cond 22
% 1.24/1.29 % AC symbols 0
% 1.24/1.29
% 1.24/1.29 % ------ Schedule dynamic 5 is on
% 1.24/1.29
% 1.24/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.24/1.29
% 1.24/1.29
% 1.24/1.29 % ------
% 1.24/1.29 % Current options:
% 1.24/1.29 % ------
% 1.24/1.29
% 1.24/1.29
% 1.24/1.29 %
% 1.24/1.29
% 1.24/1.29 % ------ Proving...
% 1.24/1.29 %
% 1.24/1.29
% 1.24/1.29 % SZS status Theorem for theBenchmark.p
% 1.24/1.29
% 1.24/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.24/1.29
% 1.24/1.29
%------------------------------------------------------------------------------