%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET628+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 : n020.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 02:47:37 PM UTC 2026
% Result : Theorem 1.91s 1.28s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 10 unt; 0 def)
% Number of atoms : 142 ( 27 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 155 ( 63 ~; 66 |; 19 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 65 !; 7 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f4,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f7,conjecture,
! [X0] :
( intersect(X0,X0)
<=> not_equal(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( intersect(X0,X0)
<=> not_equal(X0,empty_set) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0] :
( intersect(X0,X0)
<~> not_equal(X0,empty_set) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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,[],[f1]) ).
fof(f12,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,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ( member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ~ not_equal(X0,X1)
| X0 != X1 )
& ( X0 = X1
| not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f18,plain,
? [X0] :
( ( intersect(X0,X0)
| not_equal(X0,empty_set) )
& ( ~ intersect(X0,X0)
| ~ not_equal(X0,empty_set) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f19,plain,
( ( intersect(sK2,sK2)
| not_equal(sK2,empty_set) )
& ( ~ intersect(sK2,sK2)
| ~ not_equal(sK2,empty_set) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0,X1] :
( ~ not_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
( intersect(sK2,sK2)
| not_equal(sK2,empty_set) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
( ~ intersect(sK2,sK2)
| ~ not_equal(sK2,empty_set) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f28]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( not_equal(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i] : ~ not_equal(X0,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,negated_conjecture,
( ~ not_equal(sK2,empty_set)
| ~ intersect(sK2,sK2) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_59,negated_conjecture,
( not_equal(sK2,empty_set)
| intersect(sK2,sK2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_67,plain,
( ~ intersect(sK2,sK2)
| ~ not_equal(sK2,empty_set) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_68,plain,
( ~ not_equal(sK2,empty_set)
| ~ intersect(sK2,sK2) ),
inference(renaming,[status(thm)],[c_67]) ).
tcf(c_69,plain,
( intersect(sK2,sK2)
| not_equal(sK2,empty_set) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
tcf(c_70,plain,
( not_equal(sK2,empty_set)
| intersect(sK2,sK2) ),
inference(renaming,[status(thm)],[c_69]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( not_equal(X0,X1)
| ( X0 = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ intersect(sK2,sK2)
| ( X1 != empty_set )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_68]) ).
tcf(c_204,plain,
( ( sK2 = empty_set )
| ~ intersect(sK2,sK2) ),
inference(unflattening,[status(thm)],[c_203]) ).
tcf(c_211,plain,
! [X0: $i] :
( intersect(sK2,sK2)
| ( X0 != sK2 )
| ( X0 != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_70]) ).
tcf(c_212,plain,
( intersect(sK2,sK2)
| ( empty_set != sK2 ) ),
inference(unflattening,[status(thm)],[c_211]) ).
tcf(c_455,plain,
! [X0: $i] : ~ intersect(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_52]) ).
tcf(c_484,plain,
! [X0: $i] :
( member(sK1(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_54,c_52]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i] :
( intersect(X0,X1)
| ( X0 = empty_set )
| ~ member(sK1(X0,empty_set),X1) ),
inference(superposition,[status(thm)],[c_484,c_49]) ).
tcf(c_569,plain,
! [X0: $i] :
( intersect(X0,X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_484,c_515]) ).
tcf(c_579,plain,
empty_set = sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_204,c_569]) ).
tcf(c_580,plain,
intersect(sK2,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_212,c_579]) ).
tcf(c_586,plain,
! [X0: $i] : ~ intersect(sK2,X0),
inference(demodulation,[status(thm)],[c_455,c_579]) ).
tcf(c_588,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_580,c_586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n020.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 11:31:05 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.91/1.28 % SZS status Started for theBenchmark.p
% 1.91/1.28 % SZS status Theorem for theBenchmark.p
% 1.91/1.28
% 1.91/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.91/1.28
% 1.91/1.28 % ------ iProver source info
% 1.91/1.28
% 1.91/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.91/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.91/1.28 % git: non_committed_changes: false
% 1.91/1.28
% 1.91/1.28 % ------ Parsing...
% 1.91/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.91/1.28
% 1.91/1.28 % ------ 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 %
% 1.91/1.28
% 1.91/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.91/1.28
% 1.91/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.91/1.28 % ------ Proving...
% 1.91/1.28 % ------ Problem Properties
% 1.91/1.28
% 1.91/1.28 %
% 1.91/1.28 % clauses 9
% 1.91/1.28 % conjectures 0
% 1.91/1.28 % EPR 5
% 1.91/1.28 % Horn 8
% 1.91/1.28 % unary 1
% 1.91/1.28 % binary 5
% 1.91/1.28 % lits 20
% 1.91/1.28 % lits eq 4
% 1.91/1.28 % fd_pure 0
% 1.91/1.28 % fd_pseudo 0
% 1.91/1.28 % fd_cond 0
% 1.91/1.28 % fd_pseudo_cond 2
% 1.91/1.28 % AC symbols 0
% 1.91/1.28
% 1.91/1.28 % ------ Schedule dynamic 5 is on
% 1.91/1.28
% 1.91/1.28 % ------ no conjectures: strip conj schedule
% 1.91/1.28
% 1.91/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.91/1.28
% 1.91/1.28
% 1.91/1.28 % ------
% 1.91/1.28 % Current options:
% 1.91/1.28 % ------
% 1.91/1.28
% 1.91/1.28
% 1.91/1.28 %
% 1.91/1.28
% 1.91/1.28 % ------ Proving...
% 1.91/1.28 %
% 1.91/1.28
% 1.91/1.28 % SZS status Theorem for theBenchmark.p
% 1.91/1.28
% 1.91/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.91/1.28
% 1.91/1.28
%------------------------------------------------------------------------------