%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET909+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 : n013.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 02:49:05 PM UTC 2026
% Result : Theorem 0.51s 11.29s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 22 unt; 2 def)
% Number of atoms : 183 ( 78 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 209 ( 80 ~; 81 |; 43 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 88 !; 11 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,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] :
( 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(f13,conjecture,
! [X0,X1,X2] : set_union2(unordered_pair(X0,X1),X2) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] : set_union2(unordered_pair(X0,X1),X2) != empty_set,
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f19,plain,
? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X0,X1),X2),
inference(ennf_transformation,[],[f14]) ).
fof(f20,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f4]) ).
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,[],[f5]) ).
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] :
( ( 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,[],[f6]) ).
fof(f28,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,[],[f27]) ).
fof(f29,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,[],[f28]) ).
fof(f30,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(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f29]) ).
fof(f33,plain,
empty_set = set_union2(unordered_pair(sK5,sK6),sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f19]) ).
fof(f36,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
empty_set = set_union2(unordered_pair(sK5,sK6),sK7),
inference(cnf_transformation,[],[f33]) ).
fof(f58,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f37]) ).
fof(f61,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f40]) ).
fof(f62,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f61]) ).
fof(f64,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f47]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_53,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f58]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f62]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_72,negated_conjecture,
set_union2(unordered_pair(sK5,sK6),sK7) = empty_set,
inference(cnf_transformation,[],[f57]) ).
tcf(c_189,plain,
set_union2(sK7,unordered_pair(sK5,sK6)) = empty_set,
inference(demodulation,[status(thm)],[c_72,c_51]) ).
tcf(c_261,definition,
iPr_def_10 = unordered_pair(sK5,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_262,definition,
iPr_def_11 = set_union2(sK7,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_263,plain,
iPr_def_11 = empty_set,
inference(demodulation,[status(thm)],[c_189,c_261,c_262]) ).
tcf(c_544,plain,
! [X0: $i] : ~ in(X0,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_53,c_263]) ).
tcf(c_545,plain,
in(sK6,iPr_def_10),
inference(superposition,[status(thm)],[c_261,c_58]) ).
tcf(c_547,plain,
set_union2(iPr_def_10,sK7) = iPr_def_11,
inference(demodulation,[status(thm)],[c_262,c_51]) ).
tcf(c_612,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_547,c_63]) ).
tcf(c_616,plain,
! [X0: $i] : ~ in(X0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_612,c_544]) ).
tcf(c_619,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_545,c_616]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET909+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.39 % Computer : n013.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Thu Sep 24 12:21:18 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 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
% 0.15/10.44
% 0.15/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.44
% 0.15/10.44 % Detected problem language: tptp
% 0.15/10.45 % Proving...
% 0.51/11.29 % SZS status Started for theBenchmark.p
% 0.51/11.29 % SZS status Theorem for theBenchmark.p
% 0.51/11.29
% 0.51/11.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.51/11.29
% 0.51/11.29 % ------ iProver source info
% 0.51/11.29
% 0.51/11.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.51/11.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.51/11.29 % git: non_committed_changes: false
% 0.51/11.29
% 0.51/11.29 % ------ Parsing...
% 0.51/11.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.51/11.29
% 0.51/11.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.51/11.29
% 0.51/11.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.51/11.29
% 0.51/11.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.51/11.29 % ------ Proving...
% 0.51/11.29 % ------ Problem Properties
% 0.51/11.29
% 0.51/11.29 %
% 0.51/11.29 % clauses 26
% 0.51/11.29 % conjectures 0
% 0.51/11.29 % EPR 6
% 0.51/11.29 % Horn 21
% 0.51/11.29 % unary 12
% 0.51/11.29 % binary 6
% 0.51/11.29 % lits 50
% 0.51/11.29 % lits eq 19
% 0.51/11.29 % fd_pure 0
% 0.51/11.29 % fd_pseudo 0
% 0.51/11.29 % fd_cond 1
% 0.51/11.29 % fd_pseudo_cond 6
% 0.51/11.29 % AC symbols 0
% 0.51/11.29
% 0.51/11.29 % ------ Schedule dynamic 5 is on
% 0.51/11.29
% 0.51/11.29 % ------ no conjectures: strip conj schedule
% 0.51/11.29
% 0.51/11.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.51/11.29
% 0.51/11.29
% 0.51/11.29 % ------
% 0.51/11.29 % Current options:
% 0.51/11.29 % ------
% 0.51/11.29
% 0.51/11.29
% 0.51/11.29 %
% 0.51/11.29
% 0.51/11.29 % ------ Proving...
% 0.51/11.29 %
% 0.51/11.29
% 0.51/11.29 % SZS status Theorem for theBenchmark.p
% 0.51/11.29
% 0.51/11.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.51/11.29
% 0.51/11.29
%------------------------------------------------------------------------------