%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 02:48:53 PM UTC 2026
% Result : Theorem 2.00s 1.49s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 20 unt; 2 def)
% Number of atoms : 234 ( 154 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 237 ( 92 ~; 95 |; 44 &)
% ( 5 <=>; 1 =>; 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; 5 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn 103 !; 9 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,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(f6,axiom,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != unordered_pair(X1,X2)
& X0 != singleton(X2)
& X0 != singleton(X1)
& X0 != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& subset(unordered_pair(X0,X1),unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& subset(unordered_pair(X0,X1),unordered_pair(X2,X3)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f16,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f10]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( X0 != X3
& X0 != X2
& subset(unordered_pair(X0,X1),unordered_pair(X2,X3)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] :
( unordered_pair(X1,X2) != singleton(X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK0(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f21]) ).
fof(f23,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,[],[f4]) ).
fof(f24,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,[],[f23]) ).
fof(f25,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,[],[f24]) ).
fof(f26,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(sK1(X0,X1,X2),X2)
| sK1(X0,X1,X2) = X1
| sK1(X0,X1,X2) = X0 )
& ( ~ in(sK1(X0,X1,X2),X2)
| ( sK1(X0,X1,X2) != X1
& sK1(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ~ subset(X0,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 )
& ( ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 )
| subset(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ~ subset(X0,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 )
& ( ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 )
| subset(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
( sK4 != sK7
& sK4 != sK6
& subset(unordered_pair(sK4,sK5),unordered_pair(sK6,sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f18]) ).
fof(f34,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ subset(X0,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f52,plain,
sK4 != sK7,
inference(cnf_transformation,[],[f31]) ).
fof(f53,plain,
sK4 != sK6,
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
subset(unordered_pair(sK4,sK5),unordered_pair(sK6,sK7)),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X2,X0,X1] :
( unordered_pair(X1,X2) != singleton(X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f56,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f34]) ).
fof(f57,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f38]) ).
fof(f58,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f57]) ).
tcf(c_52,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f56]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f58]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( singleton(X2) = X0 )
| ( singleton(X1) = X0 )
| ( unordered_pair(X1,X2) = X0 )
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( X0 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_69,negated_conjecture,
subset(unordered_pair(sK4,sK5),unordered_pair(sK6,sK7)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_70,negated_conjecture,
sK4 != sK6,
inference(cnf_transformation,[],[f53]) ).
tcf(c_71,negated_conjecture,
sK4 != sK7,
inference(cnf_transformation,[],[f52]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(X0,X1) != singleton(X2) ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_531,definition,
iPr_def_10 = unordered_pair(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_532,definition,
iPr_def_11 = unordered_pair(sK6,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_533,negated_conjecture,
sK4 != sK7,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_534,negated_conjecture,
sK4 != sK6,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_535,negated_conjecture,
subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_69,c_532,c_531]) ).
tcf(c_791,plain,
in(sK4,iPr_def_10),
inference(superposition,[status(thm)],[c_531,c_56]) ).
tcf(c_834,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( singleton(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_531,c_72]) ).
tcf(c_973,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK4 )
| ( X0 = sK4 )
| ( unordered_pair(X0,X1) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_531,c_68]) ).
tcf(c_1103,plain,
( ( sK4 = sK7 )
| ( sK4 = sK6 )
| ( iPr_def_10 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_532,c_973]) ).
tcf(c_1104,plain,
iPr_def_10 != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_1103,c_533,c_534]) ).
tcf(c_1263,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( singleton(sK7) = X0 )
| ( singleton(sK6) = X0 )
| ( unordered_pair(sK6,sK7) = X0 )
| ~ subset(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_532,c_64]) ).
tcf(c_1264,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ( X0 = empty_set )
| ( singleton(sK7) = X0 )
| ( singleton(sK6) = X0 )
| ~ subset(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1263,c_532]) ).
tcf(c_1751,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( empty_set = iPr_def_10 )
| ( singleton(sK7) = iPr_def_10 )
| ( singleton(sK6) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_535,c_1264]) ).
tcf(c_1755,plain,
( ( empty_set = iPr_def_10 )
| ( singleton(sK7) = iPr_def_10 )
| ( singleton(sK6) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1751,c_1104]) ).
tcf(c_1768,plain,
( ( sK4 = sK7 )
| ( empty_set = iPr_def_10 )
| ( singleton(sK6) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1755,c_834]) ).
tcf(c_1772,plain,
( ( empty_set = iPr_def_10 )
| ( singleton(sK6) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1768,c_533]) ).
tcf(c_1784,plain,
( ( sK4 = sK6 )
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1772,c_834]) ).
tcf(c_1788,plain,
empty_set = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_1784,c_534]) ).
tcf(c_1810,plain,
! [X0: $i] : ~ in(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_52,c_1788]) ).
tcf(c_1812,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_791,c_1810]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.57 % Computer : n005.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Thu Sep 24 12:19:48 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.61 Running first-order theorem proving
% 0.10/0.61 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
% 0.10/0.62
% 0.10/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.62
% 0.10/0.63 % Detected problem language: tptp
% 0.15/0.64 % Proving...
% 2.00/1.49 % SZS status Started for theBenchmark.p
% 2.00/1.49 % SZS status Theorem for theBenchmark.p
% 2.00/1.49
% 2.00/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.00/1.49
% 2.00/1.49 % ------ iProver source info
% 2.00/1.49
% 2.00/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 2.00/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.00/1.49 % git: non_committed_changes: false
% 2.00/1.49
% 2.00/1.49 % ------ Parsing...
% 2.00/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.00/1.49
% 2.00/1.49 % ------ Preprocessing... sup_sim: 0 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 %
% 2.00/1.49
% 2.00/1.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.00/1.49
% 2.00/1.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.00/1.49 % ------ Proving...
% 2.00/1.49 % ------ Problem Properties
% 2.00/1.49
% 2.00/1.49 %
% 2.00/1.49 % clauses 25
% 2.00/1.49 % conjectures 3
% 2.00/1.49 % EPR 9
% 2.00/1.49 % Horn 20
% 2.00/1.49 % unary 16
% 2.00/1.49 % binary 3
% 2.00/1.49 % lits 43
% 2.00/1.49 % lits eq 24
% 2.00/1.49 % fd_pure 0
% 2.00/1.49 % fd_pseudo 0
% 2.00/1.49 % fd_cond 1
% 2.00/1.49 % fd_pseudo_cond 6
% 2.00/1.49 % AC symbols 0
% 2.00/1.49
% 2.00/1.49 % ------ Schedule dynamic 5 is on
% 2.00/1.49
% 2.00/1.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.00/1.49
% 2.00/1.49
% 2.00/1.49 % ------
% 2.00/1.49 % Current options:
% 2.00/1.49 % ------
% 2.00/1.49
% 2.00/1.49
% 2.00/1.49 %
% 2.00/1.49
% 2.00/1.49 % ------ Proving...
% 2.00/1.49 %
% 2.00/1.49
% 2.00/1.49 % SZS status Theorem for theBenchmark.p
% 2.00/1.49
% 2.00/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.00/1.49
% 2.00/1.49
%------------------------------------------------------------------------------