%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET593+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 : n016.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 02:47:29 PM UTC 2026
% Result : Theorem 3.54s 1.08s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 10 unt; 3 def)
% Number of atoms : 218 ( 3 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 167 ( 65 ~; 76 |; 19 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 95 !; 5 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,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(f3,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] :
( subset(X0,union(X1,X2))
=> ( subset(difference(X0,X2),X1)
& subset(difference(X0,X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th52) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,union(X1,X2))
=> ( subset(difference(X0,X2),X1)
& subset(difference(X0,X1),X2) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0,X1,X2] :
( subset(X0,union(X1,X2))
& ( ~ subset(difference(X0,X2),X1)
| ~ subset(difference(X0,X1),X2) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f13,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,[],[f2]) ).
fof(f14,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,[],[f13]) ).
fof(f15,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,[],[f9]) ).
fof(f16,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,[],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f21,plain,
( subset(sK2,union(sK3,sK4))
& ( ~ subset(difference(sK2,sK4),sK3)
| ~ subset(difference(sK2,sK3),sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f10]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
subset(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
( ~ subset(difference(sK2,sK4),sK3)
| ~ subset(difference(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
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(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_62,negated_conjecture,
( ~ subset(difference(sK2,sK4),sK3)
| ~ subset(difference(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_63,negated_conjecture,
subset(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_199,definition,
iPr_def_10 = union(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_200,definition,
iPr_def_11 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_201,definition,
iPr_def_12 = difference(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_202,negated_conjecture,
subset(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_63,c_199]) ).
tcf(c_203,negated_conjecture,
( ~ subset(iPr_def_12,sK3)
| ~ subset(iPr_def_11,sK4) ),
inference(demodulation,[status(thm)],[c_62,c_201,c_200]) ).
tcf(c_440,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_199,c_49]) ).
tcf(c_459,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_200,c_53]) ).
tcf(c_460,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_201,c_53]) ).
tcf(c_487,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_200,c_54]) ).
tcf(c_488,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_12)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_201,c_54]) ).
tcf(c_518,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK2) ),
inference(superposition,[status(thm)],[c_56,c_459]) ).
tcf(c_526,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| member(sK0(iPr_def_12,X0),sK2) ),
inference(superposition,[status(thm)],[c_56,c_460]) ).
tcf(c_572,plain,
! [X0: $i] :
( member(X0,sK4)
| member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_199,c_51]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_11,X1)
| member(sK0(iPr_def_11,X1),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_518,c_57]) ).
tcf(c_614,plain,
( subset(iPr_def_11,sK4)
| member(sK0(iPr_def_11,sK4),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_12,X1)
| member(sK0(iPr_def_12,X1),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_526,c_57]) ).
tcf(c_1738,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK4)
| member(sK0(iPr_def_11,X0),sK3)
| ~ subset(sK2,iPr_def_10) ),
inference(superposition,[status(thm)],[c_592,c_572]) ).
tcf(c_1777,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK4)
| member(sK0(iPr_def_11,X0),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1738,c_202]) ).
tcf(c_1813,plain,
( subset(iPr_def_11,sK4)
| member(sK0(iPr_def_11,sK4),sK3) ),
inference(superposition,[status(thm)],[c_1777,c_55]) ).
tcf(c_1862,plain,
( subset(iPr_def_11,sK4)
| ~ member(sK0(iPr_def_11,sK4),iPr_def_11) ),
inference(superposition,[status(thm)],[c_1813,c_487]) ).
tcf(c_1863,plain,
( subset(iPr_def_11,sK4)
| member(sK0(iPr_def_11,sK4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_1813,c_440]) ).
tcf(c_1936,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| member(sK0(iPr_def_12,X0),sK4)
| member(sK0(iPr_def_12,X0),sK3)
| ~ subset(sK2,iPr_def_10) ),
inference(superposition,[status(thm)],[c_817,c_572]) ).
tcf(c_1975,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| member(sK0(iPr_def_12,X0),sK4)
| member(sK0(iPr_def_12,X0),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1936,c_202]) ).
tcf(c_2104,plain,
subset(iPr_def_11,sK4),
inference(global_subsumption_just,[status(thm)],[c_1863,c_614,c_1862]) ).
tcf(c_2106,plain,
~ subset(iPr_def_12,sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_203,c_2104]) ).
tcf(c_2116,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| member(sK0(iPr_def_12,X0),sK3)
| ~ member(sK0(iPr_def_12,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_1975,c_488]) ).
tcf(c_2241,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| member(sK0(iPr_def_12,X0),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2116,c_56]) ).
tcf(c_2249,plain,
subset(iPr_def_12,sK3),
inference(superposition,[status(thm)],[c_2241,c_55]) ).
tcf(c_2254,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2249,c_2106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET593+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n016.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Thu Sep 24 11:27:42 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.54/1.08 % SZS status Started for theBenchmark.p
% 3.54/1.08 % SZS status Theorem for theBenchmark.p
% 3.54/1.08
% 3.54/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.54/1.08
% 3.54/1.08 % ------ iProver source info
% 3.54/1.08
% 3.54/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 3.54/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.54/1.08 % git: non_committed_changes: false
% 3.54/1.08
% 3.54/1.08 % ------ Parsing...
% 3.54/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.54/1.08
% 3.54/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.54/1.08
% 3.54/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.54/1.08
% 3.54/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.54/1.08 % ------ Proving...
% 3.54/1.08 % ------ Problem Properties
% 3.54/1.08
% 3.54/1.08 %
% 3.54/1.08 % clauses 18
% 3.54/1.08 % conjectures 2
% 3.54/1.08 % EPR 4
% 3.54/1.08 % Horn 14
% 3.54/1.08 % unary 6
% 3.54/1.08 % binary 7
% 3.54/1.08 % lits 35
% 3.54/1.08 % lits eq 6
% 3.54/1.08 % fd_pure 0
% 3.54/1.08 % fd_pseudo 0
% 3.54/1.08 % fd_cond 0
% 3.54/1.08 % fd_pseudo_cond 2
% 3.54/1.08 % AC symbols 0
% 3.54/1.08
% 3.54/1.08 % ------ Schedule dynamic 5 is on
% 3.54/1.08
% 3.54/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.54/1.08
% 3.54/1.08
% 3.54/1.08 % ------
% 3.54/1.08 % Current options:
% 3.54/1.08 % ------
% 3.54/1.08
% 3.54/1.08
% 3.54/1.08 %
% 3.54/1.08
% 3.54/1.08 % ------ Proving...
% 3.54/1.08 %
% 3.54/1.08
% 3.54/1.08 % SZS status Theorem for theBenchmark.p
% 3.54/1.08
% 3.54/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.54/1.08
% 3.54/1.08
%------------------------------------------------------------------------------