%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET918+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 : n026.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 02:49:06 PM UTC 2026
% Result : Theorem 2.24s 1.27s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 24 unt; 3 def)
% Number of atoms : 233 ( 105 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 264 ( 99 ~; 101 |; 58 &)
% ( 6 <=>; 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 : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 0 sgn 94 !; 11 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
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_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,conjecture,
! [X0,X1,X2] :
~ ( X0 != X1
& in(X1,X2)
& set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( X0 != X1
& in(X1,X2)
& set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f14,plain,
? [X0,X1,X2] :
( X0 != X1
& in(X1,X2)
& set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,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,[],[f4]) ).
fof(f16,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,[],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,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(f19,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,[],[f18]) ).
fof(f20,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,[],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f24]) ).
fof(f28,plain,
( sK5 != sK6
& in(sK6,sK7)
& singleton(sK5) = set_intersection2(unordered_pair(sK5,sK6),sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f14]) ).
fof(f31,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f51,plain,
sK5 != sK6,
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
in(sK6,sK7),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
singleton(sK5) = set_intersection2(unordered_pair(sK5,sK6),sK7),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f32]) ).
fof(f59,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f37]) ).
fof(f60,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f59]) ).
fof(f62,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f44]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f60]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_71,negated_conjecture,
set_intersection2(unordered_pair(sK5,sK6),sK7) = singleton(sK5),
inference(cnf_transformation,[],[f53]) ).
tcf(c_72,negated_conjecture,
in(sK6,sK7),
inference(cnf_transformation,[],[f52]) ).
tcf(c_73,negated_conjecture,
sK5 != sK6,
inference(cnf_transformation,[],[f51]) ).
tcf(c_191,plain,
set_intersection2(sK7,unordered_pair(sK5,sK6)) = singleton(sK5),
inference(demodulation,[status(thm)],[c_71,c_51]) ).
tcf(c_466,definition,
iPr_def_10 = unordered_pair(sK5,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_467,definition,
iPr_def_11 = set_intersection2(sK7,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_468,definition,
iPr_def_12 = singleton(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_469,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_191,c_468,c_466,c_467]) ).
tcf(c_470,negated_conjecture,
sK5 != sK6,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_471,negated_conjecture,
in(sK6,sK7),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_760,plain,
singleton(sK5) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_468,c_469]) ).
tcf(c_762,plain,
in(sK6,iPr_def_10),
inference(superposition,[status(thm)],[c_466,c_60]) ).
tcf(c_764,plain,
set_intersection2(iPr_def_10,sK7) = iPr_def_11,
inference(demodulation,[status(thm)],[c_467,c_51]) ).
tcf(c_792,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_760,c_55]) ).
tcf(c_830,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK7) ),
inference(superposition,[status(thm)],[c_764,c_65]) ).
tcf(c_883,plain,
( in(sK6,iPr_def_11)
| ~ in(sK6,sK7) ),
inference(superposition,[status(thm)],[c_762,c_830]) ).
tcf(c_885,plain,
in(sK6,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_883,c_471]) ).
tcf(c_889,plain,
sK5 = sK6,
inference(superposition,[status(thm)],[c_885,c_792]) ).
tcf(c_890,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_889,c_470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET918+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:25:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.24/1.27 % SZS status Started for theBenchmark.p
% 2.24/1.27 % SZS status Theorem for theBenchmark.p
% 2.24/1.27
% 2.24/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.24/1.27
% 2.24/1.27 % ------ iProver source info
% 2.24/1.27
% 2.24/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.24/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.24/1.27 % git: non_committed_changes: false
% 2.24/1.27
% 2.24/1.27 % ------ Parsing...
% 2.24/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.24/1.27
% 2.24/1.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.24/1.27
% 2.24/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.24/1.27
% 2.24/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.24/1.27 % ------ Proving...
% 2.24/1.27 % ------ Problem Properties
% 2.24/1.27
% 2.24/1.27 %
% 2.24/1.27 % clauses 27
% 2.24/1.27 % conjectures 2
% 2.24/1.27 % EPR 5
% 2.24/1.27 % Horn 22
% 2.24/1.27 % unary 13
% 2.24/1.27 % binary 4
% 2.24/1.27 % lits 53
% 2.24/1.27 % lits eq 26
% 2.24/1.27 % fd_pure 0
% 2.24/1.27 % fd_pseudo 0
% 2.24/1.27 % fd_cond 0
% 2.24/1.27 % fd_pseudo_cond 8
% 2.24/1.27 % AC symbols 0
% 2.24/1.27
% 2.24/1.27 % ------ Schedule dynamic 5 is on
% 2.24/1.27
% 2.24/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.24/1.27
% 2.24/1.27
% 2.24/1.27 % ------
% 2.24/1.27 % Current options:
% 2.24/1.27 % ------
% 2.24/1.27
% 2.24/1.27
% 2.24/1.27 %
% 2.24/1.27
% 2.24/1.27 % ------ Proving...
% 2.24/1.27 %
% 2.24/1.27
% 2.24/1.27 % SZS status Theorem for theBenchmark.p
% 2.24/1.27
% 2.24/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.24/1.28
% 2.24/1.28
%------------------------------------------------------------------------------