%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET632+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 : n006.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 02:47:38 PM UTC 2026
% Result : Theorem 0.42s 11.50s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 20 unt; 0 def)
% Number of atoms : 179 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 187 ( 78 ~; 68 |; 31 &)
% ( 5 <=>; 5 =>; 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 111 !; 11 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f6,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X2)
& subset(X0,X1) )
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th114) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X2)
& subset(X0,X1) )
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ~ intersect(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f15,plain,
? [X0,X1,X2] :
( disjoint(X1,X2)
& subset(X0,X2)
& subset(X0,X1)
& empty_set != X0 ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
? [X0,X1,X2] :
( disjoint(X1,X2)
& subset(X0,X2)
& subset(X0,X1)
& empty_set != X0 ),
inference(flattening,[],[f15]) ).
fof(f17,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,[],[f12]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ? [X2] :
( member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ? [X3] :
( member(X3,X1)
& member(X3,X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ( member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( disjoint(sK3,sK4)
& subset(sK2,sK4)
& subset(sK2,sK3)
& empty_set != sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f16]) ).
fof(f26,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
disjoint(sK3,sK4),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
subset(sK2,sK4),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_55,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,negated_conjecture,
empty_set != sK2,
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f41]) ).
tcf(c_64,negated_conjecture,
subset(sK2,sK4),
inference(cnf_transformation,[],[f40]) ).
tcf(c_65,negated_conjecture,
disjoint(sK3,sK4),
inference(cnf_transformation,[],[f39]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( ~ intersect(X0,X1)
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_65]) ).
tcf(c_173,plain,
~ intersect(sK3,sK4),
inference(unflattening,[status(thm)],[c_172]) ).
tcf(c_271,negated_conjecture,
subset(sK2,sK4),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_272,negated_conjecture,
subset(sK2,sK3),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_273,negated_conjecture,
empty_set != sK2,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_454,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_55]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK0(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK1(X2,X0),X1)
| ~ intersect(X2,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_51]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X0,X2)
| subset(X0,X1)
| ~ member(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50,c_52]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X0,X2)
| ~ intersect(X0,X1)
| ~ member(sK1(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_518,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_454,c_57]) ).
tcf(c_573,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X0,X1)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_479,c_497]) ).
tcf(c_630,plain,
( intersect(sK3,sK4)
| ~ intersect(sK4,sK3) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_726,plain,
! [X0: $i] :
( intersect(sK2,sK4)
| subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_271,c_573]) ).
tcf(c_761,plain,
( intersect(sK2,sK4)
| ( empty_set = sK2 ) ),
inference(superposition,[status(thm)],[c_726,c_518]) ).
tcf(c_764,plain,
intersect(sK2,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_761,c_273]) ).
tcf(c_767,plain,
intersect(sK4,sK2),
inference(superposition,[status(thm)],[c_764,c_60]) ).
tcf(c_785,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X2,X1)
| ~ intersect(X2,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_481,c_498]) ).
tcf(c_902,plain,
! [X0: $i] :
( intersect(X0,sK3)
| ~ intersect(X0,sK2) ),
inference(superposition,[status(thm)],[c_272,c_785]) ).
tcf(c_929,plain,
intersect(sK4,sK3),
inference(superposition,[status(thm)],[c_767,c_902]) ).
tcf(c_930,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_929,c_630,c_173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET632+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.58 % Computer : n006.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Thu Sep 24 11:31:12 UTC 2026
% 0.10/10.58 % CPUTime :
% 0.10/10.59 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.62 Running first-order theorem proving
% 0.14/10.62 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
% 0.14/10.63
% 0.14/10.63 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.63
% 0.14/10.63 % Detected problem language: tptp
% 0.14/10.65 % Proving...
% 0.42/11.50 % SZS status Started for theBenchmark.p
% 0.42/11.50 % SZS status Theorem for theBenchmark.p
% 0.42/11.50
% 0.42/11.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.42/11.50
% 0.42/11.50 % ------ iProver source info
% 0.42/11.50
% 0.42/11.50 % git: date: 2026-07-19 20:42:38 +0200
% 0.42/11.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.42/11.50 % git: non_committed_changes: false
% 0.42/11.50
% 0.42/11.50 % ------ Parsing...
% 0.42/11.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.42/11.50
% 0.42/11.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 0.42/11.50
% 0.42/11.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.42/11.50
% 0.42/11.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.42/11.50 % ------ Proving...
% 0.42/11.50 % ------ Problem Properties
% 0.42/11.50
% 0.42/11.50 %
% 0.42/11.50 % clauses 14
% 0.42/11.50 % conjectures 3
% 0.42/11.50 % EPR 10
% 0.42/11.50 % Horn 13
% 0.42/11.50 % unary 6
% 0.42/11.50 % binary 5
% 0.42/11.50 % lits 25
% 0.42/11.50 % lits eq 2
% 0.42/11.50 % fd_pure 0
% 0.42/11.50 % fd_pseudo 0
% 0.42/11.50 % fd_cond 0
% 0.42/11.50 % fd_pseudo_cond 1
% 0.42/11.50 % AC symbols 0
% 0.42/11.50
% 0.42/11.50 % ------ Schedule dynamic 5 is on
% 0.42/11.50
% 0.42/11.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.42/11.50
% 0.42/11.50
% 0.42/11.50 % ------
% 0.42/11.50 % Current options:
% 0.42/11.50 % ------
% 0.42/11.50
% 0.42/11.50
% 0.42/11.50 %
% 0.42/11.50
% 0.42/11.50 % ------ Proving...
% 0.42/11.50 %
% 0.42/11.50
% 0.42/11.50 % SZS status Theorem for theBenchmark.p
% 0.42/11.50
% 0.42/11.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.16/11.50
% 2.16/11.50
%------------------------------------------------------------------------------