%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 3.08s 11.30s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 5 unt; 1 def)
% Number of atoms : 219 ( 18 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 206 ( 84 ~; 83 |; 29 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 91 !; 11 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( ~ member(X3,X2)
& member(X3,X1) ) )
=> X0 = difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th20) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( ~ member(X3,X2)
& member(X3,X1) ) )
=> X0 = difference(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f8,plain,
? [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( ~ member(X3,X2)
& member(X3,X1) ) )
& difference(X1,X2) != X0 ),
inference(ennf_transformation,[],[f6]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ! [X3] :
( ( ~ member(X3,X0)
| ( ~ member(X3,X2)
& member(X3,X1) ) )
& ( member(X3,X2)
| ~ member(X3,X1)
| member(X3,X0) ) )
& difference(X1,X2) != X0 ),
inference(nnf_transformation,[],[f8]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ! [X3] :
( ( ~ member(X3,X0)
| ( ~ member(X3,X2)
& member(X3,X1) ) )
& ( member(X3,X2)
| ~ member(X3,X1)
| member(X3,X0) ) )
& difference(X1,X2) != X0 ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( ! [X3] :
( ( ~ member(X3,sK1)
| ( ~ member(X3,sK3)
& member(X3,sK2) ) )
& ( member(X3,sK3)
| ~ member(X3,sK2)
| member(X3,sK1) ) )
& sK1 != difference(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X3] :
( ~ member(X3,sK1)
| ~ member(X3,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X3] :
( ~ member(X3,sK1)
| member(X3,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X3] :
( member(X3,sK3)
| ~ member(X3,sK2)
| member(X3,sK1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
sK1 != difference(sK2,sK3),
inference(cnf_transformation,[],[f18]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_59,negated_conjecture,
difference(sK2,sK3) != sK1,
inference(cnf_transformation,[],[f32]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( member(X0,sK3)
| member(X0,sK1)
| ~ member(X0,sK2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( ~ member(X0,sK3)
| ~ member(X0,sK1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_276,definition,
iPr_def_10 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_277,negated_conjecture,
! [X0: $i] :
( ~ member(X0,sK3)
| ~ member(X0,sK1) ),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_278,negated_conjecture,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK1) ),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_279,negated_conjecture,
! [X0: $i] :
( member(X0,sK3)
| member(X0,sK1)
| ~ member(X0,sK2) ),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_280,negated_conjecture,
iPr_def_10 != sK1,
inference(demodulation,[status(thm)],[c_59,c_276]) ).
tcf(c_495,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_276,c_50]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,difference(X1,X2))
| member(sK0(X0,difference(X1,X2)),X2)
| ~ member(sK0(X0,difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_49,c_55]) ).
tcf(c_518,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_276,c_51]) ).
tcf(c_548,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK2) ),
inference(superposition,[status(thm)],[c_56,c_495]) ).
tcf(c_566,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK3)
| member(sK0(iPr_def_10,X0),sK1) ),
inference(superposition,[status(thm)],[c_548,c_279]) ).
tcf(c_575,plain,
( ( iPr_def_10 = sK1 )
| ~ subset(iPr_def_10,sK1)
| ~ subset(sK1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_601,plain,
( subset(iPr_def_10,sK1)
| member(sK0(iPr_def_10,sK1),iPr_def_10) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_602,plain,
( subset(iPr_def_10,sK1)
| ~ member(sK0(iPr_def_10,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_618,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK1)
| ~ member(sK0(iPr_def_10,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_566,c_518]) ).
tcf(c_628,plain,
( subset(iPr_def_10,sK1)
| member(sK0(iPr_def_10,sK1),sK1)
| ~ member(sK0(iPr_def_10,sK1),iPr_def_10) ),
inference(instantiation,[status(thm)],[c_618]) ).
tcf(c_755,plain,
( subset(sK1,iPr_def_10)
| member(sK0(sK1,iPr_def_10),sK1) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_886,plain,
( member(sK0(sK1,iPr_def_10),sK2)
| ~ member(sK0(sK1,iPr_def_10),sK1) ),
inference(instantiation,[status(thm)],[c_278]) ).
tcf(c_887,plain,
( ~ member(sK0(sK1,iPr_def_10),sK3)
| ~ member(sK0(sK1,iPr_def_10),sK1) ),
inference(instantiation,[status(thm)],[c_277]) ).
tcf(c_920,plain,
! [X0: $i] :
( subset(X0,difference(sK2,sK3))
| member(sK0(X0,difference(sK2,sK3)),sK3)
| ~ member(sK0(X0,iPr_def_10),sK2) ),
inference(superposition,[status(thm)],[c_276,c_506]) ).
tcf(c_934,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| member(sK0(X0,iPr_def_10),sK3)
| ~ member(sK0(X0,iPr_def_10),sK2) ),
inference(light_normalisation,[status(thm)],[c_920,c_276]) ).
tcf(c_954,plain,
( subset(sK1,iPr_def_10)
| member(sK0(sK1,iPr_def_10),sK3)
| ~ member(sK0(sK1,iPr_def_10),sK2) ),
inference(instantiation,[status(thm)],[c_934]) ).
tcf(c_955,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_954,c_886,c_887,c_755,c_628,c_601,c_602,c_575,c_280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/10.39 % Computer : n015.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Thu Sep 24 11:23:37 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.16/10.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/10.43 Running first-order theorem proving
% 0.16/10.43 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
% 0.16/10.44
% 0.16/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.44
% 0.16/10.45 % Detected problem language: tptp
% 0.16/10.46 % Proving...
% 3.08/11.30 % SZS status Started for theBenchmark.p
% 3.08/11.30 % SZS status Theorem for theBenchmark.p
% 3.08/11.30
% 3.08/11.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.08/11.30
% 3.08/11.30 % ------ iProver source info
% 3.08/11.30
% 3.08/11.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.08/11.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.08/11.30 % git: non_committed_changes: false
% 3.08/11.30
% 3.08/11.30 % ------ Parsing...
% 3.08/11.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.08/11.30
% 3.08/11.30 % ------ 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 %
% 3.08/11.30
% 3.08/11.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.08/11.30
% 3.08/11.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.08/11.30 % ------ Proving...
% 3.08/11.30 % ------ Problem Properties
% 3.08/11.30
% 3.08/11.30 %
% 3.08/11.30 % clauses 13
% 3.08/11.30 % conjectures 4
% 3.08/11.30 % EPR 7
% 3.08/11.30 % Horn 10
% 3.08/11.30 % unary 3
% 3.08/11.30 % binary 6
% 3.08/11.30 % lits 27
% 3.08/11.30 % lits eq 3
% 3.08/11.30 % fd_pure 0
% 3.08/11.30 % fd_pseudo 0
% 3.08/11.30 % fd_cond 0
% 3.08/11.30 % fd_pseudo_cond 1
% 3.08/11.30 % AC symbols 0
% 3.08/11.30
% 3.08/11.30 % ------ Schedule dynamic 5 is on
% 3.08/11.30
% 3.08/11.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.08/11.30
% 3.08/11.30
% 3.08/11.30 % ------
% 3.08/11.30 % Current options:
% 3.08/11.30 % ------
% 3.08/11.30
% 3.08/11.30
% 3.08/11.30 %
% 3.08/11.30
% 3.08/11.30 % ------ Proving...
% 3.08/11.30 %
% 3.08/11.30
% 3.08/11.30 % SZS status Theorem for theBenchmark.p
% 3.08/11.30
% 3.08/11.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.08/11.30
% 3.08/11.30
%------------------------------------------------------------------------------