%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 02:46:00 PM UTC 2026
% Result : Unsatisfiable 3.01s 1.30s
% Output : CNFRefutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 141 ( 64 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 75 ( 0 sgn 75 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).
fof(f2,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom1) ).
fof(f11,axiom,
! [X2,X0,X1] :
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom2) ).
fof(f12,axiom,
! [X2,X0,X1] :
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X0)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom3) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',not_member_of_difference) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference_or_set2) ).
fof(f19,axiom,
difference(a,b,aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_b) ).
fof(f20,axiom,
difference(a,aDb,aD_aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_aDb) ).
fof(f21,negated_conjecture,
~ intersection(a,b,aD_aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2)
| member(h(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2)
| member(h(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X2)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| member(X3,X1)
| ~ member(X3,X0)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_88,plain,
difference(a,b,aDb),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
difference(a,aDb,aD_aDb),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
~ intersection(a,b,aD_aDb),
inference(cnf_transformation,[],[f21]) ).
tcf(c_376,plain,
( ~ member(h(a,b,aD_aDb),aD_aDb)
| ~ member(h(a,b,aD_aDb),b)
| ~ member(h(a,b,aD_aDb),a) ),
inference(resolution,[status(thm)],[c_90,c_81]) ).
tcf(c_386,plain,
( member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),b) ),
inference(resolution,[status(thm)],[c_90,c_80]) ).
tcf(c_393,plain,
( member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),a) ),
inference(resolution,[status(thm)],[c_90,c_79]) ).
tcf(c_1275,plain,
! [X0: $i,X1: $i] :
( member(h(a,b,aD_aDb),X1)
| member(h(a,b,aD_aDb),X0)
| ~ difference(a,X0,X1)
| ~ member(h(a,b,aD_aDb),a) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_1288,plain,
! [X0: $i,X1: $i] :
( ~ difference(X1,b,X0)
| ~ member(h(a,b,aD_aDb),b)
| ~ member(h(a,b,aD_aDb),X0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_1295,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(h(a,b,aD_aDb),X2)
| member(h(a,b,aD_aDb),X1)
| ~ difference(X0,X1,X2)
| ~ member(h(a,b,aD_aDb),X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_1297,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ difference(X2,X0,X1)
| ~ member(h(a,b,aD_aDb),X1)
| ~ member(h(a,b,aD_aDb),X0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_1298,plain,
! [X0: $i,X1: $i] :
( member(h(a,b,aD_aDb),X1)
| ~ subset(X0,X1)
| ~ member(h(a,b,aD_aDb),X0) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_1362,plain,
( ~ difference(a,b,aDb)
| ~ member(h(a,b,aD_aDb),aDb)
| ~ member(h(a,b,aD_aDb),b) ),
inference(instantiation,[status(thm)],[c_1288]) ).
tcf(c_1430,plain,
! [X0: $i] :
( member(h(a,b,aD_aDb),b)
| member(h(a,b,aD_aDb),X0)
| ~ difference(a,b,X0)
| ~ member(h(a,b,aD_aDb),a) ),
inference(instantiation,[status(thm)],[c_1275]) ).
tcf(c_1596,plain,
( ~ difference(a,aDb,aD_aDb)
| ~ member(h(a,b,aD_aDb),aD_aDb)
| ~ member(h(a,b,aD_aDb),aDb) ),
inference(instantiation,[status(thm)],[c_1297]) ).
tcf(c_1740,plain,
! [X0: $i] :
( member(X0,a)
| ~ member(X0,aD_aDb) ),
inference(superposition,[status(thm)],[c_89,c_82]) ).
tcf(c_1913,plain,
( member(h(a,b,aD_aDb),aDb)
| member(h(a,b,aD_aDb),b)
| ~ difference(a,b,aDb)
| ~ member(h(a,b,aD_aDb),a) ),
inference(instantiation,[status(thm)],[c_1430]) ).
tcf(c_1928,plain,
! [X0: $i,X1: $i] :
( member(h(a,b,aD_aDb),aDb)
| member(h(a,b,aD_aDb),X1)
| ~ difference(X0,aDb,X1)
| ~ member(h(a,b,aD_aDb),X0) ),
inference(instantiation,[status(thm)],[c_1295]) ).
tcf(c_1977,plain,
! [X0: $i] :
( subset(aD_aDb,X0)
| member(member_of_1_not_of_2(aD_aDb,X0),a) ),
inference(superposition,[status(thm)],[c_71,c_1740]) ).
tcf(c_2072,plain,
subset(aD_aDb,a),
inference(superposition,[status(thm)],[c_1977,c_72]) ).
tcf(c_2930,plain,
! [X0: $i] :
( member(h(a,b,aD_aDb),X0)
| ~ subset(aD_aDb,X0)
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(instantiation,[status(thm)],[c_1298]) ).
tcf(c_2931,plain,
( member(h(a,b,aD_aDb),a)
| ~ subset(aD_aDb,a)
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(instantiation,[status(thm)],[c_2930]) ).
tcf(c_3234,plain,
! [X0: $i] :
( member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),aDb)
| ~ difference(X0,aDb,aD_aDb)
| ~ member(h(a,b,aD_aDb),X0) ),
inference(instantiation,[status(thm)],[c_1928]) ).
tcf(c_3235,plain,
( member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),aDb)
| ~ difference(a,aDb,aD_aDb)
| ~ member(h(a,b,aD_aDb),a) ),
inference(instantiation,[status(thm)],[c_3234]) ).
tcf(c_3236,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3235,c_2931,c_2072,c_1913,c_1596,c_1362,c_393,c_386,c_376,c_88,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 09:06:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 3.01/1.30 % SZS status Started for theBenchmark.p
% 3.01/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.01/1.30
% 3.01/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.01/1.30
% 3.01/1.30 % ------ iProver source info
% 3.01/1.30
% 3.01/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.01/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.01/1.30 % git: non_committed_changes: false
% 3.01/1.30
% 3.01/1.30 % ------ Parsing...% successful
% 3.01/1.30
% 3.01/1.30
% 3.01/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.01/1.30
% 3.01/1.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.01/1.30
% 3.01/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.01/1.30 % ------ Proving...
% 3.01/1.30 % ------ Problem Properties
% 3.01/1.30
% 3.01/1.30 %
% 3.01/1.30 % clauses 18
% 3.01/1.30 % conjectures 1
% 3.01/1.30 % EPR 10
% 3.01/1.30 % Horn 11
% 3.01/1.30 % unary 3
% 3.01/1.30 % binary 2
% 3.01/1.30 % lits 50
% 3.01/1.30 % lits eq 0
% 3.01/1.30 % fd_pure 0
% 3.01/1.30 % fd_pseudo 0
% 3.01/1.30 % fd_cond 0
% 3.01/1.30 % fd_pseudo_cond 0
% 3.01/1.30 % AC symbols 0
% 3.01/1.30
% 3.01/1.30 % ------ Schedule dynamic 5 is on
% 3.01/1.30
% 3.01/1.30 % ------ no equalities: superposition off
% 3.01/1.30
% 3.01/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.01/1.30
% 3.01/1.30
% 3.01/1.30 % ------
% 3.01/1.30 % Current options:
% 3.01/1.30 % ------
% 3.01/1.30
% 3.01/1.30
% 3.01/1.30 %
% 3.01/1.30
% 3.01/1.30 % ------ Proving...
% 3.01/1.30 %
% 3.01/1.30
% 3.01/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.01/1.30
% 3.01/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.01/1.30
% 3.01/1.30
%------------------------------------------------------------------------------