%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET701+4 : 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 : n002.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 02:47:49 PM UTC 2026
% Result : Theorem 5.74s 2.26s
% Output : CNFRefutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 68 ( 4 unt; 0 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 224 ( 89 ~; 93 |; 31 &)
% ( 6 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 126 !; 18 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f12,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI35) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( subset(X1,X3)
& subset(X0,X3)
& ( subset(X0,X1)
<~> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( subset(X1,X3)
& subset(X0,X3)
& ( subset(X0,X1)
<~> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
? [X0,X1,X2,X3] :
( subset(X1,X3)
& subset(X0,X3)
& ( subset(X0,X1)
| subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) )
& ( ~ subset(X0,X1)
| ~ subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( subset(X1,X3)
& subset(X0,X3)
& ( subset(X0,X1)
| subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) )
& ( ~ subset(X0,X1)
| ~ subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( subset(sK1,sK3)
& subset(sK0,sK3)
& ( subset(sK0,sK1)
| subset(intersection(sK0,difference(sK3,sK1)),intersection(sK2,difference(sK3,sK2))) )
& ( ~ subset(sK0,sK1)
| ~ subset(intersection(sK0,difference(sK3,sK1)),intersection(sK2,difference(sK3,sK2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f18]) ).
fof(f20,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,[],[f16]) ).
fof(f21,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,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK4(X0,X1),X0)
& ~ member(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f25]) ).
fof(f28,plain,
subset(sK0,sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
( subset(sK0,sK1)
| subset(intersection(sK0,difference(sK3,sK1)),intersection(sK2,difference(sK3,sK2))) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
( ~ subset(sK0,sK1)
| ~ subset(intersection(sK0,difference(sK3,sK1)),intersection(sK2,difference(sK3,sK2))) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,negated_conjecture,
( ~ subset(sK0,sK1)
| ~ subset(intersection(sK0,difference(sK3,sK1)),intersection(sK2,difference(sK3,sK2))) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,negated_conjecture,
( subset(sK0,sK1)
| subset(intersection(sK0,difference(sK3,sK1)),intersection(sK2,difference(sK3,sK2))) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_51,negated_conjecture,
subset(sK0,sK3),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_172,plain,
( subset(sK0,sK1)
| ~ member(sK4(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_173,plain,
( subset(sK0,sK1)
| member(sK4(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_188,plain,
! [X0: $i] :
( member(sK4(sK0,sK1),X0)
| ~ subset(sK0,X0)
| ~ member(sK4(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_189,plain,
( member(sK4(sK0,sK1),sK3)
| ~ subset(sK0,sK3)
| ~ member(sK4(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_188]) ).
tcf(c_191,plain,
! [X0: $i] :
( member(sK4(sK0,sK1),intersection(sK0,X0))
| ~ member(sK4(sK0,sK1),sK0)
| ~ member(sK4(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK0,sK1),X1)
| ~ subset(X0,X1)
| ~ member(sK4(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK0,sK1),X1)
| member(sK4(sK0,sK1),difference(X0,X1))
| ~ member(sK4(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] :
( ~ member(sK4(sK0,sK1),X1)
| ~ member(sK4(sK0,sK1),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK0,sK1),X1)
| ~ member(sK4(sK0,sK1),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK0,sK1),X0)
| ~ member(sK4(sK0,sK1),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK4(sK0,sK1),difference(X1,X2))
| ~ member(sK4(sK0,sK1),intersection(X0,difference(X1,X2))) ),
inference(instantiation,[status(thm)],[c_246]) ).
tcf(c_394,plain,
! [X0: $i] :
( member(sK4(sK0,sK1),sK1)
| member(sK4(sK0,sK1),difference(X0,sK1))
| ~ member(sK4(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_240]) ).
tcf(c_395,plain,
( member(sK4(sK0,sK1),sK1)
| member(sK4(sK0,sK1),difference(sK3,sK1))
| ~ member(sK4(sK0,sK1),sK3) ),
inference(instantiation,[status(thm)],[c_394]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X1),X2)
| member(sK4(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_54,c_57]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X1),X2)
| member(sK4(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_54,c_58]) ).
tcf(c_648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(intersection(X0,X2),X3)
| member(sK4(intersection(X0,X2),X3),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_412,c_55]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK0,sK1),intersection(sK0,difference(X0,X1)))
| ~ member(sK4(sK0,sK1),sK0)
| ~ member(sK4(sK0,sK1),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_191]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK4(sK0,sK1),intersection(X1,difference(X2,X3)))
| ~ member(sK4(sK0,sK1),X0)
| ~ subset(X0,intersection(X1,difference(X2,X3))) ),
inference(instantiation,[status(thm)],[c_239]) ).
tcf(c_944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(intersection(X0,difference(X1,X2)),X3)
| ~ member(sK4(intersection(X0,difference(X1,X2)),X3),X2) ),
inference(superposition,[status(thm)],[c_481,c_61]) ).
tcf(c_1340,plain,
! [X0: $i] :
( member(sK4(sK0,sK1),intersection(sK0,difference(X0,sK1)))
| ~ member(sK4(sK0,sK1),sK0)
| ~ member(sK4(sK0,sK1),difference(X0,sK1)) ),
inference(instantiation,[status(thm)],[c_748]) ).
tcf(c_1341,plain,
( member(sK4(sK0,sK1),intersection(sK0,difference(sK3,sK1)))
| ~ member(sK4(sK0,sK1),sK0)
| ~ member(sK4(sK0,sK1),difference(sK3,sK1)) ),
inference(instantiation,[status(thm)],[c_1340]) ).
tcf(c_3042,plain,
( member(sK4(sK0,sK1),intersection(sK2,difference(sK3,sK2)))
| ~ member(sK4(sK0,sK1),intersection(sK0,difference(sK3,sK1)))
| ~ subset(intersection(sK0,difference(sK3,sK1)),intersection(sK2,difference(sK3,sK2))) ),
inference(instantiation,[status(thm)],[c_752]) ).
tcf(c_3179,plain,
( member(sK4(sK0,sK1),difference(sK3,sK2))
| ~ member(sK4(sK0,sK1),intersection(sK2,difference(sK3,sK2))) ),
inference(instantiation,[status(thm)],[c_317]) ).
tcf(c_10474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(intersection(X0,difference(X2,X1)),X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_648,c_944]) ).
tcf(c_10712,plain,
( ~ member(sK4(sK0,sK1),sK2)
| ~ member(sK4(sK0,sK1),difference(sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_243]) ).
tcf(c_19545,plain,
( member(sK4(sK0,sK1),sK2)
| ~ member(sK4(sK0,sK1),intersection(sK2,difference(sK3,sK2))) ),
inference(instantiation,[status(thm)],[c_247]) ).
tcf(c_19830,plain,
~ subset(sK0,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_10474]) ).
tcf(c_19842,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_19830,c_19545,c_10712,c_3179,c_3042,c_1341,c_395,c_189,c_173,c_172,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET701+4 : 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 : n002.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 11:45:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 5.74/2.26 % SZS status Started for theBenchmark.p
% 5.74/2.26 % SZS status Theorem for theBenchmark.p
% 5.74/2.26
% 5.74/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.74/2.26
% 5.74/2.26 % ------ iProver source info
% 5.74/2.26
% 5.74/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 5.74/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.74/2.26 % git: non_committed_changes: false
% 5.74/2.26
% 5.74/2.26 % ------ Parsing...
% 5.74/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.74/2.26
% 5.74/2.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 5.74/2.26
% 5.74/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 5.74/2.26 % ------ Proving...
% 5.74/2.26 % ------ Problem Properties
% 5.74/2.26
% 5.74/2.26 %
% 5.74/2.26 % clauses 13
% 5.74/2.26 % conjectures 4
% 5.74/2.26 % EPR 3
% 5.74/2.26 % Horn 10
% 5.74/2.26 % unary 2
% 5.74/2.26 % binary 8
% 5.74/2.26 % lits 27
% 5.74/2.26 % lits eq 0
% 5.74/2.26 % fd_pure 0
% 5.74/2.26 % fd_pseudo 0
% 5.74/2.26 % fd_cond 0
% 5.74/2.26 % fd_pseudo_cond 0
% 5.74/2.26 % AC symbols 0
% 5.74/2.26
% 5.74/2.26 % ------ Schedule dynamic 5 is on
% 5.74/2.26
% 5.74/2.26 % ------ no equalities: superposition off
% 5.74/2.26
% 5.74/2.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.74/2.26
% 5.74/2.26
% 5.74/2.26 % ------
% 5.74/2.26 % Current options:
% 5.74/2.26 % ------
% 5.74/2.26
% 5.74/2.26
% 5.74/2.26 %
% 5.74/2.26
% 5.74/2.26 % ------ Proving...
% 5.74/2.26 %
% 5.74/2.26
% 5.74/2.26 % SZS status Theorem for theBenchmark.p
% 5.74/2.26
% 5.74/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.74/2.27
% 5.74/2.27
%------------------------------------------------------------------------------