%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET901+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 : n006.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 02:49:04 PM UTC 2026
% Result : Theorem 2.64s 6.54s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 23 unt; 3 def)
% Number of atoms : 242 ( 131 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 207 ( 81 ~; 92 |; 29 &)
% ( 4 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 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; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 1 sgn 55 !; 9 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f6,conjecture,
! [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',t42_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != unordered_pair(X1,X2)
& X0 != singleton(X2)
& X0 != singleton(X1)
& X0 != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,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(f9,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f2]) ).
fof(f10,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,[],[f7]) ).
fof(f11,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,[],[f8]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 )
& ( ~ subset(X0,unordered_pair(X1,X2))
| ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 )
& ( ~ subset(X0,unordered_pair(X1,X2))
| ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
( ( subset(sK2,unordered_pair(sK3,sK4))
| sK2 = unordered_pair(sK3,sK4)
| sK2 = singleton(sK4)
| sK2 = singleton(sK3)
| empty_set = sK2 )
& ( ~ subset(sK2,unordered_pair(sK3,sK4))
| ( sK2 != unordered_pair(sK3,sK4)
& sK2 != singleton(sK4)
& sK2 != singleton(sK3)
& empty_set != sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f15]) ).
fof(f17,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,[],[f11]) ).
fof(f18,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,[],[f17]) ).
fof(f20,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f24,plain,
( subset(sK2,unordered_pair(sK3,sK4))
| sK2 = unordered_pair(sK3,sK4)
| sK2 = singleton(sK4)
| sK2 = singleton(sK3)
| empty_set = sK2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| sK2 != unordered_pair(sK3,sK4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| sK2 != singleton(sK4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| sK2 != singleton(sK3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| empty_set != sK2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,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,[],[f18]) ).
fof(f31,plain,
! [X2,X0,X1] :
( singleton(X2) != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X2,X0,X1] :
( singleton(X1) != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X2,X0,X1] :
( empty_set != X0
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X2,X1] : subset(empty_set,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f33]) ).
fof(f35,plain,
! [X2,X1] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f32]) ).
fof(f36,plain,
! [X2,X1] : subset(singleton(X2),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f20]) ).
tcf(c_54,negated_conjecture,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| ( empty_set != sK2 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_55,negated_conjecture,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| ( singleton(sK3) != sK2 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_56,negated_conjecture,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| ( singleton(sK4) != sK2 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_57,negated_conjecture,
( ~ subset(sK2,unordered_pair(sK3,sK4))
| ( unordered_pair(sK3,sK4) != sK2 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_58,negated_conjecture,
( subset(sK2,unordered_pair(sK3,sK4))
| ( empty_set = sK2 )
| ( singleton(sK4) = sK2 )
| ( singleton(sK3) = sK2 )
| ( unordered_pair(sK3,sK4) = sK2 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : subset(empty_set,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : subset(singleton(X0),unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : subset(singleton(X0),unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_63,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,[],[f29]) ).
tcf(c_177,plain,
! [X0: $i] :
( ( X0 != sK2 )
| ( unordered_pair(sK3,sK4) != sK2 )
| ( unordered_pair(sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_57]) ).
tcf(c_178,plain,
unordered_pair(sK3,sK4) != sK2,
inference(unflattening,[status(thm)],[c_177]) ).
tcf(c_337,plain,
( subset(sK2,unordered_pair(sK3,sK4))
| ( empty_set = sK2 )
| ( singleton(sK4) = sK2 )
| ( singleton(sK3) = sK2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_178]) ).
tcf(c_786,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_787,definition,
iPr_def_11 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_788,definition,
iPr_def_12 = unordered_pair(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_789,plain,
( subset(sK2,iPr_def_12)
| ( iPr_def_11 = sK2 )
| ( iPr_def_10 = sK2 )
| ( empty_set = sK2 ) ),
inference(demodulation,[status(thm)],[c_337,c_788,c_787,c_786]) ).
tcf(c_790,plain,
iPr_def_12 != sK2,
inference(demodulation,[status(thm)],[c_178]) ).
tcf(c_791,negated_conjecture,
( ~ subset(sK2,iPr_def_12)
| ( iPr_def_11 != sK2 ) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_792,negated_conjecture,
( ~ subset(sK2,iPr_def_12)
| ( iPr_def_10 != sK2 ) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_793,negated_conjecture,
( ~ subset(sK2,iPr_def_12)
| ( empty_set != sK2 ) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_996,plain,
! [X0: $i] : subset(iPr_def_10,unordered_pair(sK3,X0)),
inference(superposition,[status(thm)],[c_786,c_60]) ).
tcf(c_1001,plain,
! [X0: $i] : subset(iPr_def_11,unordered_pair(X0,sK4)),
inference(superposition,[status(thm)],[c_787,c_61]) ).
tcf(c_1005,plain,
subset(empty_set,iPr_def_12),
inference(superposition,[status(thm)],[c_788,c_59]) ).
tcf(c_1007,plain,
subset(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_788,c_996]) ).
tcf(c_1008,plain,
subset(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_788,c_1001]) ).
tcf(c_1045,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( singleton(sK4) = X0 )
| ( singleton(sK3) = X0 )
| ( unordered_pair(sK3,sK4) = X0 )
| ~ subset(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_788,c_63]) ).
tcf(c_1062,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ( X0 = iPr_def_11 )
| ( X0 = iPr_def_10 )
| ( X0 = empty_set )
| ~ subset(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_1045,c_786,c_787,c_788]) ).
tcf(c_1089,plain,
( ( sK2 = iPr_def_12 )
| ( sK2 = iPr_def_11 )
| ( sK2 = iPr_def_10 )
| ( empty_set = sK2 ) ),
inference(superposition,[status(thm)],[c_789,c_1062]) ).
tcf(c_1133,plain,
( subset(sK2,iPr_def_12)
| ( sK2 = iPr_def_12 )
| ( sK2 = iPr_def_11 )
| ( sK2 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1089,c_1005]) ).
tcf(c_1136,plain,
( ( sK2 = iPr_def_12 )
| ( sK2 = iPr_def_11 )
| ( sK2 = iPr_def_10 )
| ~ subset(sK2,iPr_def_12) ),
inference(superposition,[status(thm)],[c_1089,c_793]) ).
tcf(c_1149,plain,
( ( sK2 = iPr_def_12 )
| ( sK2 = iPr_def_11 )
| ( sK2 = iPr_def_10 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1133,c_1136]) ).
tcf(c_1163,plain,
( ( sK2 = iPr_def_11 )
| ( sK2 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1149,c_790]) ).
tcf(c_1175,plain,
( ( sK2 = iPr_def_10 )
| ~ subset(sK2,iPr_def_12) ),
inference(superposition,[status(thm)],[c_1163,c_791]) ).
tcf(c_1185,plain,
( ( sK2 = iPr_def_10 )
| ~ subset(iPr_def_11,iPr_def_12) ),
inference(superposition,[status(thm)],[c_1163,c_1175]) ).
tcf(c_1186,plain,
sK2 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_1185,c_1008]) ).
tcf(c_1190,plain,
( ~ subset(iPr_def_10,iPr_def_12)
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_792,c_1186]) ).
tcf(c_1193,plain,
~ subset(iPr_def_10,iPr_def_12),
inference(equality_resolution_simp,[status(thm)],[c_1190]) ).
tcf(c_1194,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1193,c_1007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/5.46 % Computer : n006.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Thu Sep 24 12:20:51 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/5.52 Running first-order theorem proving
% 0.23/5.52 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
% 0.23/5.54
% 0.23/5.54 % ======== iProver multi-core TPTP/SMT =========
% 0.23/5.54
% 0.23/5.54 % Detected problem language: tptp
% 0.23/5.56 % Proving...
% 2.64/6.54 % SZS status Started for theBenchmark.p
% 2.64/6.54 % SZS status Theorem for theBenchmark.p
% 2.64/6.54
% 2.64/6.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.64/6.54
% 2.64/6.54 % ------ iProver source info
% 2.64/6.54
% 2.64/6.54 % git: date: 2026-07-19 20:42:38 +0200
% 2.64/6.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.64/6.54 % git: non_committed_changes: false
% 2.64/6.54
% 2.64/6.54 % ------ Parsing...
% 2.64/6.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.64/6.54
% 2.64/6.54 % ------ 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 %
% 2.64/6.54
% 2.64/6.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.64/6.54
% 2.64/6.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.64/6.54 % ------ Proving...
% 2.64/6.54 % ------ Problem Properties
% 2.64/6.54
% 2.64/6.54 %
% 2.64/6.54 % clauses 17
% 2.64/6.54 % conjectures 3
% 2.64/6.54 % EPR 9
% 2.64/6.54 % Horn 15
% 2.64/6.54 % unary 12
% 2.64/6.54 % binary 3
% 2.64/6.54 % lits 27
% 2.64/6.54 % lits eq 15
% 2.64/6.54 % fd_pure 0
% 2.64/6.54 % fd_pseudo 0
% 2.64/6.54 % fd_cond 0
% 2.64/6.54 % fd_pseudo_cond 1
% 2.64/6.54 % AC symbols 0
% 2.64/6.54
% 2.64/6.54 % ------ Schedule dynamic 5 is on
% 2.64/6.54
% 2.64/6.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.64/6.54
% 2.64/6.54
% 2.64/6.54 % ------
% 2.64/6.54 % Current options:
% 2.64/6.54 % ------
% 2.64/6.54
% 2.64/6.54
% 2.64/6.54 %
% 2.64/6.54
% 2.64/6.54 % ------ Proving...
% 2.64/6.54 %
% 2.64/6.54
% 2.64/6.54 % SZS status Theorem for theBenchmark.p
% 2.64/6.54
% 2.64/6.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.64/6.54
% 2.64/6.54
%------------------------------------------------------------------------------