%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET009+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 : 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 02:45:59 PM UTC 2026
% Result : Theorem 0.90s 1.26s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 10 unt; 2 def)
% Number of atoms : 133 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 44 ~; 44 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 74 !; 5 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f4,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_difference) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f7,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& ~ subset(difference(X2,X1),difference(X2,X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f8,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(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(flattening,[],[f8]) ).
fof(f10,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,[],[f6]) ).
fof(f11,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,[],[f10]) ).
fof(f12,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))],[f11]) ).
fof(f13,plain,
( subset(sK1,sK2)
& ~ subset(difference(sK3,sK2),difference(sK3,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f7]) ).
fof(f14,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f16,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
~ subset(difference(sK3,sK2),difference(sK3,sK1)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_56,negated_conjecture,
~ subset(difference(sK3,sK2),difference(sK3,sK1)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_57,negated_conjecture,
subset(sK1,sK2),
inference(cnf_transformation,[],[f21]) ).
tcf(c_142,definition,
iPr_def_10 = difference(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_143,definition,
iPr_def_11 = difference(sK3,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_144,negated_conjecture,
subset(sK1,sK2),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_145,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_56,c_143,c_142]) ).
tcf(c_300,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_142,c_50]) ).
tcf(c_315,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK3) ),
inference(superposition,[status(thm)],[c_53,c_300]) ).
tcf(c_340,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_52]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(difference(X0,X1),X2)
| ~ member(sK0(difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_53,c_51]) ).
tcf(c_559,plain,
! [X0: $i] :
( subset(iPr_def_10,difference(sK3,X0))
| member(sK0(iPr_def_10,difference(sK3,X0)),X0) ),
inference(superposition,[status(thm)],[c_315,c_340]) ).
tcf(c_1081,plain,
! [X0: $i] :
( subset(difference(sK3,sK2),X0)
| ~ member(sK0(iPr_def_10,X0),sK2) ),
inference(superposition,[status(thm)],[c_142,c_350]) ).
tcf(c_1086,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ member(sK0(iPr_def_10,X0),sK2) ),
inference(light_normalisation,[status(thm)],[c_1081,c_142]) ).
tcf(c_1503,plain,
( subset(iPr_def_10,difference(sK3,sK1))
| member(sK0(iPr_def_10,iPr_def_11),sK1) ),
inference(superposition,[status(thm)],[c_143,c_559]) ).
tcf(c_1516,plain,
( subset(iPr_def_10,iPr_def_11)
| member(sK0(iPr_def_10,iPr_def_11),sK1) ),
inference(light_normalisation,[status(thm)],[c_1503,c_143]) ).
tcf(c_1517,plain,
member(sK0(iPr_def_10,iPr_def_11),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_1516,c_145]) ).
tcf(c_1550,plain,
! [X0: $i] :
( member(sK0(iPr_def_10,iPr_def_11),X0)
| ~ subset(sK1,X0) ),
inference(superposition,[status(thm)],[c_1517,c_54]) ).
tcf(c_1598,plain,
( subset(iPr_def_10,iPr_def_11)
| ~ subset(sK1,sK2) ),
inference(superposition,[status(thm)],[c_1550,c_1086]) ).
tcf(c_1599,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1598,c_145,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.41 % Computer : n015.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Thu Sep 24 09:07:26 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.45 Running first-order theorem proving
% 0.19/0.45 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
% 0.19/0.46
% 0.19/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.19/0.46
% 0.19/0.46 % Detected problem language: tptp
% 0.19/0.48 % Proving...
% 0.90/1.26 % SZS status Started for theBenchmark.p
% 0.90/1.26 % SZS status Theorem for theBenchmark.p
% 0.90/1.26
% 0.90/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.90/1.26
% 0.90/1.26 % ------ iProver source info
% 0.90/1.26
% 0.90/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 0.90/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.90/1.26 % git: non_committed_changes: false
% 0.90/1.26
% 0.90/1.26 % ------ Parsing...
% 0.90/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.90/1.26
% 0.90/1.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.90/1.26
% 0.90/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.90/1.26
% 0.90/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.90/1.26 % ------ Proving...
% 0.90/1.26 % ------ Problem Properties
% 0.90/1.26
% 0.90/1.26 %
% 0.90/1.26 % clauses 11
% 0.90/1.26 % conjectures 2
% 0.90/1.26 % EPR 4
% 0.90/1.26 % Horn 9
% 0.90/1.26 % unary 5
% 0.90/1.26 % binary 4
% 0.90/1.26 % lits 19
% 0.90/1.26 % lits eq 2
% 0.90/1.26 % fd_pure 0
% 0.90/1.26 % fd_pseudo 0
% 0.90/1.26 % fd_cond 0
% 0.90/1.26 % fd_pseudo_cond 0
% 0.90/1.26 % AC symbols 0
% 0.90/1.26
% 0.90/1.26 % ------ Schedule dynamic 5 is on
% 0.90/1.26
% 0.90/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.90/1.26
% 0.90/1.26
% 0.90/1.26 % ------
% 0.90/1.26 % Current options:
% 0.90/1.26 % ------
% 0.90/1.26
% 0.90/1.26
% 0.90/1.26 %
% 0.90/1.26
% 0.90/1.26 % ------ Proving...
% 0.90/1.26 %
% 0.90/1.26
% 0.90/1.26 % SZS status Theorem for theBenchmark.p
% 0.90/1.26
% 0.90/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.90/1.26
% 0.90/1.26
%------------------------------------------------------------------------------