%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET589+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 02:47:28 PM UTC 2026
% Result : Theorem 1.94s 1.28s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 13 unt; 2 def)
% Number of atoms : 146 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 45 ~; 46 |; 19 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 75 !; 10 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f7,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(difference(X0,X3),difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th48) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(difference(X0,X3),difference(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& ~ subset(difference(X0,X3),difference(X1,X2)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& ~ subset(difference(X0,X3),difference(X1,X2)) ),
inference(flattening,[],[f14]) ).
fof(f16,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,[],[f4]) ).
fof(f17,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,[],[f16]) ).
fof(f18,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,[],[f13]) ).
fof(f19,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,[],[f18]) ).
fof(f20,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))],[f19]) ).
fof(f21,plain,
( subset(sK3,sK4)
& subset(sK1,sK2)
& ~ subset(difference(sK1,sK4),difference(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f15]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
~ subset(difference(sK1,sK4),difference(sK2,sK3)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,negated_conjecture,
~ subset(difference(sK1,sK4),difference(sK2,sK3)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,negated_conjecture,
subset(sK1,sK2),
inference(cnf_transformation,[],[f33]) ).
tcf(c_61,negated_conjecture,
subset(sK3,sK4),
inference(cnf_transformation,[],[f32]) ).
tcf(c_116,definition,
iPr_def_10 = difference(sK1,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_117,definition,
iPr_def_11 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_118,negated_conjecture,
subset(sK3,sK4),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_119,negated_conjecture,
subset(sK1,sK2),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_120,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_59,c_117,c_116]) ).
tcf(c_307,plain,
! [X0: $i] :
( member(X0,sK1)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_116,c_53]) ).
tcf(c_342,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_116,c_54]) ).
tcf(c_405,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK1) ),
inference(superposition,[status(thm)],[c_56,c_307]) ).
tcf(c_433,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ member(sK0(iPr_def_10,X0),sK4) ),
inference(superposition,[status(thm)],[c_56,c_342]) ).
tcf(c_502,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK1) ),
inference(superposition,[status(thm)],[c_119,c_57]) ).
tcf(c_503,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_118,c_57]) ).
tcf(c_541,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| member(X0,sK3)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_117,c_52]) ).
tcf(c_572,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK2) ),
inference(superposition,[status(thm)],[c_405,c_502]) ).
tcf(c_833,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),iPr_def_11)
| member(sK0(iPr_def_10,X0),sK3) ),
inference(superposition,[status(thm)],[c_572,c_541]) ).
tcf(c_1313,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),iPr_def_11)
| member(sK0(iPr_def_10,X0),sK4) ),
inference(superposition,[status(thm)],[c_833,c_503]) ).
tcf(c_1332,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_1313,c_433,c_1313]) ).
tcf(c_1338,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1332,c_55]) ).
tcf(c_1341,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1338,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:22:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 1.94/1.28 % SZS status Started for theBenchmark.p
% 1.94/1.28 % SZS status Theorem for theBenchmark.p
% 1.94/1.28
% 1.94/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.94/1.28
% 1.94/1.28 % ------ iProver source info
% 1.94/1.28
% 1.94/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.94/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.94/1.28 % git: non_committed_changes: false
% 1.94/1.28
% 1.94/1.28 % ------ Parsing...
% 1.94/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.94/1.28
% 1.94/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.94/1.28
% 1.94/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.94/1.28
% 1.94/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.94/1.28 % ------ Proving...
% 1.94/1.28 % ------ Problem Properties
% 1.94/1.28
% 1.94/1.28 %
% 1.94/1.28 % clauses 15
% 1.94/1.28 % conjectures 3
% 1.94/1.28 % EPR 6
% 1.94/1.28 % Horn 13
% 1.94/1.28 % unary 6
% 1.94/1.28 % binary 6
% 1.94/1.28 % lits 27
% 1.94/1.28 % lits eq 2
% 1.94/1.28 % fd_pure 0
% 1.94/1.28 % fd_pseudo 0
% 1.94/1.28 % fd_cond 0
% 1.94/1.28 % fd_pseudo_cond 0
% 1.94/1.28 % AC symbols 0
% 1.94/1.28
% 1.94/1.28 % ------ Schedule dynamic 5 is on
% 1.94/1.28
% 1.94/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.94/1.28
% 1.94/1.28
% 1.94/1.28 % ------
% 1.94/1.28 % Current options:
% 1.94/1.28 % ------
% 1.94/1.28
% 1.94/1.28
% 1.94/1.28 %
% 1.94/1.28
% 1.94/1.28 % ------ Proving...
% 1.94/1.28 %
% 1.94/1.28
% 1.94/1.28 % SZS status Theorem for theBenchmark.p
% 1.94/1.28
% 1.94/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.94/1.28
% 1.94/1.28
%------------------------------------------------------------------------------