%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:47:26 PM UTC 2026
% Result : Theorem 3.00s 6.30s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 8 unt; 1 def)
% Number of atoms : 198 ( 37 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 194 ( 77 ~; 82 |; 27 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 78 !; 11 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
& member(X3,X1) ) )
=> X0 = intersection(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th19) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
& member(X3,X1) ) )
=> X0 = intersection(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
& member(X3,X1) ) )
& intersection(X1,X2) != X0 ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ! [X3] :
( ( ~ member(X3,X0)
| ( member(X3,X2)
& member(X3,X1) ) )
& ( ~ member(X3,X2)
| ~ member(X3,X1)
| member(X3,X0) ) )
& intersection(X1,X2) != X0 ),
inference(nnf_transformation,[],[f10]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ! [X3] :
( ( ~ member(X3,X0)
| ( member(X3,X2)
& member(X3,X1) ) )
& ( ~ member(X3,X2)
| ~ member(X3,X1)
| member(X3,X0) ) )
& intersection(X1,X2) != X0 ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( ! [X3] :
( ( ~ member(X3,sK2)
| ( member(X3,sK4)
& member(X3,sK3) ) )
& ( ~ member(X3,sK4)
| ~ member(X3,sK3)
| member(X3,sK2) ) )
& sK2 != intersection(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f37,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X3] :
( ~ member(X3,sK2)
| member(X3,sK4) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X3] :
( ~ member(X3,sK2)
| member(X3,sK3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X3] :
( ~ member(X3,sK4)
| ~ member(X3,sK3)
| member(X3,sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
sK2 != intersection(sK3,sK4),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,negated_conjecture,
intersection(sK3,sK4) != sK2,
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK4)
| ~ member(X0,sK3) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,sK2) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_65,negated_conjecture,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,sK2) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_334,definition,
iPr_def_10 = intersection(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_335,negated_conjecture,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,sK2) ),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_336,negated_conjecture,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,sK2) ),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_337,negated_conjecture,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK4)
| ~ member(X0,sK3) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_338,negated_conjecture,
iPr_def_10 != sK2,
inference(demodulation,[status(thm)],[c_62,c_334]) ).
tcf(c_339,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_563,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_334,c_49]) ).
tcf(c_579,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_334,c_50]) ).
tcf(c_594,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_334,c_51]) ).
tcf(c_672,plain,
! [X0: $i] :
( ( iPr_def_10 = sK2 )
| ( iPr_def_10 != X0 )
| ( sK2 != X0 ) ),
inference(instantiation,[status(thm)],[c_341]) ).
tcf(c_701,plain,
( ( iPr_def_10 = sK2 )
| ~ member(sK1(iPr_def_10,sK2),iPr_def_10)
| ~ member(sK1(iPr_def_10,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_773,plain,
! [X0: $i] :
( member(sK1(X0,sK2),sK3)
| member(sK1(X0,sK2),X0)
| ( X0 = sK2 ) ),
inference(superposition,[status(thm)],[c_61,c_336]) ).
tcf(c_774,plain,
! [X0: $i] :
( member(sK1(X0,sK2),sK4)
| member(sK1(X0,sK2),X0)
| ( X0 = sK2 ) ),
inference(superposition,[status(thm)],[c_61,c_335]) ).
tcf(c_850,plain,
( ( iPr_def_10 = sK2 )
| ( iPr_def_10 != iPr_def_10 )
| ( sK2 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_672]) ).
tcf(c_851,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_872,plain,
( member(sK1(iPr_def_10,sK2),sK2)
| ~ member(sK1(iPr_def_10,sK2),sK4)
| ~ member(sK1(iPr_def_10,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_948,plain,
( member(sK1(iPr_def_10,sK2),sK3)
| ( sK2 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_773,c_579]) ).
tcf(c_1030,plain,
( member(sK1(iPr_def_10,sK2),sK4)
| ( sK2 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_774,c_594]) ).
tcf(c_1354,plain,
member(sK1(iPr_def_10,sK2),sK3),
inference(global_subsumption_just,[status(thm)],[c_948,c_338,c_850,c_851,c_948]) ).
tcf(c_1357,plain,
( member(sK1(iPr_def_10,sK2),iPr_def_10)
| ~ member(sK1(iPr_def_10,sK2),sK4) ),
inference(superposition,[status(thm)],[c_1354,c_563]) ).
tcf(c_1366,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1357,c_1030,c_948,c_872,c_851,c_850,c_701,c_338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.39 % Computer : n005.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Thu Sep 24 11:19:53 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 3.00/6.30 % SZS status Started for theBenchmark.p
% 3.00/6.30 % SZS status Theorem for theBenchmark.p
% 3.00/6.30
% 3.00/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.00/6.30
% 3.00/6.30 % ------ iProver source info
% 3.00/6.30
% 3.00/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.00/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.00/6.30 % git: non_committed_changes: false
% 3.00/6.30
% 3.00/6.30 % ------ Parsing...
% 3.00/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.00/6.30
% 3.00/6.30 % ------ 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 %
% 3.00/6.30
% 3.00/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.00/6.30
% 3.00/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.00/6.30 % ------ Proving...
% 3.00/6.30 % ------ Problem Properties
% 3.00/6.30
% 3.00/6.30 %
% 3.00/6.30 % clauses 16
% 3.00/6.30 % conjectures 4
% 3.00/6.30 % EPR 7
% 3.00/6.30 % Horn 14
% 3.00/6.30 % unary 4
% 3.00/6.30 % binary 6
% 3.00/6.30 % lits 34
% 3.00/6.30 % lits eq 6
% 3.00/6.30 % fd_pure 0
% 3.00/6.30 % fd_pseudo 0
% 3.00/6.30 % fd_cond 0
% 3.00/6.30 % fd_pseudo_cond 3
% 3.00/6.30 % AC symbols 0
% 3.00/6.30
% 3.00/6.30 % ------ Schedule dynamic 5 is on
% 3.00/6.30
% 3.00/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.00/6.30
% 3.00/6.30
% 3.00/6.30 % ------
% 3.00/6.30 % Current options:
% 3.00/6.30 % ------
% 3.00/6.30
% 3.00/6.30
% 3.00/6.30 %
% 3.00/6.30
% 3.00/6.30 % ------ Proving...
% 3.00/6.30 %
% 3.00/6.30
% 3.00/6.30 % SZS status Theorem for theBenchmark.p
% 3.00/6.30
% 3.00/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.00/6.30
% 3.00/6.30
%------------------------------------------------------------------------------