%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV517+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 03:02:20 PM UTC 2026
% Result : Theorem 3.72s 1.37s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 8 unt; 0 def)
% Number of atoms : 176 ( 19 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 205 ( 77 ~; 69 |; 40 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 109 !; 18 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(f13,axiom,
! [X0,X1] :
( partition(X0,X1)
<=> ( ! [X2,X3] :
( ( member(X3,X0)
& member(X2,X0) )
=> ( ? [X4] :
( member(X4,X3)
& member(X4,X2) )
=> X2 = X3 ) )
& ! [X2] :
( member(X2,X1)
=> ? [X3] :
( member(X2,X3)
& member(X3,X0) ) )
& ! [X2] :
( member(X2,X0)
=> subset(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',partition) ).
fof(f20,conjecture,
! [X0,X1,X2,X3] :
( ( partition(X3,X1)
& member(X0,difference(X1,X2)) )
=> ? [X4] :
( member(X0,X4)
& member(X4,difference(X3,singleton(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_elem_in_partition) ).
fof(f21,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( partition(X3,X1)
& member(X0,difference(X1,X2)) )
=> ? [X4] :
( member(X0,X4)
& member(X4,difference(X3,singleton(X2))) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( partition(X0,X1)
<=> ( ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( ? [X7] :
( member(X7,X6)
& member(X7,X5) )
=> X5 = X6 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X3,X4)
& member(X4,X0) ) )
& ! [X2] :
( member(X2,X0)
=> subset(X2,X1) ) ) ),
inference(rectify,[],[f13]) ).
fof(f23,plain,
! [X0,X1] :
( partition(X0,X1)
=> ( ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( ? [X7] :
( member(X7,X6)
& member(X7,X5) )
=> X5 = X6 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X3,X4)
& member(X4,X0) ) )
& ! [X2] :
( member(X2,X0)
=> subset(X2,X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f25,plain,
? [X0,X1,X2,X3] :
( partition(X3,X1)
& member(X0,difference(X1,X2))
& ! [X4] :
( ~ member(X0,X4)
| ~ member(X4,difference(X3,singleton(X2))) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f26,plain,
? [X0,X1,X2,X3] :
( partition(X3,X1)
& member(X0,difference(X1,X2))
& ! [X4] :
( ~ member(X0,X4)
| ~ member(X4,difference(X3,singleton(X2))) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ~ partition(X0,X1)
| ( ! [X5,X6] :
( ~ member(X6,X0)
| ~ member(X5,X0)
| ! [X7] :
( ~ member(X7,X6)
| ~ member(X7,X5) )
| X5 = X6 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( member(X3,X4)
& member(X4,X0) ) )
& ! [X2] :
( ~ member(X2,X0)
| subset(X2,X1) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f28,plain,
! [X0,X1] :
( ~ partition(X0,X1)
| ( ! [X5,X6] :
( ~ member(X6,X0)
| ~ member(X5,X0)
| ! [X7] :
( ~ member(X7,X6)
| ~ member(X7,X5) )
| X5 = X6 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( member(X3,X4)
& member(X4,X0) ) )
& ! [X2] :
( ~ member(X2,X0)
| subset(X2,X1) ) ) ),
inference(flattening,[],[f27]) ).
fof(f30,plain,
( partition(sK3,sK1)
& member(sK0,difference(sK1,sK2))
& ! [X4] :
( ~ member(sK0,X4)
| ~ member(X4,difference(sK3,singleton(sK2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f26]) ).
fof(f31,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(f32,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,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ partition(X0,X1)
| ( ! [X5,X6] :
( ~ member(X6,X0)
| ~ member(X5,X0)
| ! [X7] :
( ~ member(X7,X6)
| ~ member(X7,X5) )
| X5 = X6 )
& ! [X3] :
( ~ member(X3,X1)
| ( member(X3,sK4(X0,X3))
& member(sK4(X0,X3),X0) ) )
& ! [X2] :
( ~ member(X2,X0)
| subset(X2,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X3))],[f28]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ member(X0,singleton(X1))
| X0 = X1 )
& ( X0 != X1
| member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f35,plain,
partition(sK3,sK1),
inference(cnf_transformation,[],[f30]) ).
fof(f36,plain,
member(sK0,difference(sK1,sK2)),
inference(cnf_transformation,[],[f30]) ).
fof(f37,plain,
! [X4] :
( ~ member(sK0,X4)
| ~ member(X4,difference(sK3,singleton(sK2))) ),
inference(cnf_transformation,[],[f30]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f42,plain,
! [X3,X0,X1] :
( ~ partition(X0,X1)
| ~ member(X3,X1)
| member(X3,sK4(X0,X3)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
! [X3,X0,X1] :
( ~ partition(X0,X1)
| ~ member(X3,X1)
| member(sK4(X0,X3),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ member(sK0,X0)
| ~ member(X0,difference(sK3,singleton(sK2))) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_50,negated_conjecture,
member(sK0,difference(sK1,sK2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_51,negated_conjecture,
partition(sK3,sK1),
inference(cnf_transformation,[],[f35]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK4(X2,X0),X2)
| ~ partition(X2,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,sK4(X2,X0))
| ~ partition(X2,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,sK4(X0,X2))
| ~ member(X2,X1)
| ( X1 != sK1 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_57]) ).
tcf(c_229,plain,
! [X0: $i] :
( member(X0,sK4(sK3,X0))
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_228]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK4(X0,X2),X0)
| ~ member(X2,X1)
| ( X1 != sK1 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).
tcf(c_238,plain,
! [X0: $i] :
( member(sK4(sK3,X0),sK3)
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_237]) ).
tcf(c_239,plain,
( member(sK4(sK3,sK0),sK3)
| ~ member(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_238]) ).
tcf(c_651,plain,
member(sK0,sK1),
inference(superposition,[status(thm)],[c_50,c_53]) ).
tcf(c_661,plain,
~ member(sK0,sK2),
inference(superposition,[status(thm)],[c_50,c_54]) ).
tcf(c_679,plain,
! [X0: $i] :
( member(X0,singleton(sK2))
| ~ member(sK0,X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_52,c_49]) ).
tcf(c_706,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ member(sK0,X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_679,c_60]) ).
tcf(c_732,plain,
( ( sK4(sK3,sK0) = sK2 )
| ~ member(sK0,sK1)
| ~ member(sK4(sK3,sK0),sK3) ),
inference(superposition,[status(thm)],[c_229,c_706]) ).
tcf(c_740,plain,
( ( sK4(sK3,sK0) = sK2 )
| ~ member(sK4(sK3,sK0),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_732,c_651]) ).
tcf(c_764,plain,
sK4(sK3,sK0) = sK2,
inference(global_subsumption_just,[status(thm)],[c_740,c_239,c_651,c_740]) ).
tcf(c_768,plain,
( member(sK0,sK2)
| ~ member(sK0,sK1) ),
inference(superposition,[status(thm)],[c_764,c_229]) ).
tcf(c_769,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_768,c_661,c_651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV517+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 14:55:06 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 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
% 0.17/0.47
% 0.17/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.47
% 0.17/0.47 % Detected problem language: tptp
% 0.17/0.48 % Proving...
% 3.72/1.37 % SZS status Started for theBenchmark.p
% 3.72/1.37 % SZS status Theorem for theBenchmark.p
% 3.72/1.37
% 3.72/1.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.72/1.37
% 3.72/1.37 % ------ iProver source info
% 3.72/1.37
% 3.72/1.37 % git: date: 2026-07-19 20:42:38 +0200
% 3.72/1.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.72/1.37 % git: non_committed_changes: false
% 3.72/1.37
% 3.72/1.37 % ------ Parsing...
% 3.72/1.37 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.72/1.37
% 3.72/1.37 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.72/1.37
% 3.72/1.37 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.72/1.37
% 3.72/1.37 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.72/1.37 % ------ Proving...
% 3.72/1.37 % ------ Problem Properties
% 3.72/1.37
% 3.72/1.37 %
% 3.72/1.37 % clauses 11
% 3.72/1.37 % conjectures 2
% 3.72/1.37 % EPR 2
% 3.72/1.37 % Horn 10
% 3.72/1.37 % unary 2
% 3.72/1.37 % binary 6
% 3.72/1.37 % lits 25
% 3.72/1.37 % lits eq 2
% 3.72/1.37 % fd_pure 0
% 3.72/1.37 % fd_pseudo 0
% 3.72/1.37 % fd_cond 0
% 3.72/1.37 % fd_pseudo_cond 2
% 3.72/1.37 % AC symbols 0
% 3.72/1.37
% 3.72/1.37 % ------ Schedule dynamic 5 is on
% 3.72/1.37
% 3.72/1.37 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.72/1.37
% 3.72/1.37
% 3.72/1.37 % ------
% 3.72/1.37 % Current options:
% 3.72/1.37 % ------
% 3.72/1.37
% 3.72/1.37
% 3.72/1.37 %
% 3.72/1.37
% 3.72/1.37 % ------ Proving...
% 3.72/1.37 %
% 3.72/1.37
% 3.72/1.37 % SZS status Theorem for theBenchmark.p
% 3.72/1.37
% 3.72/1.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.72/1.37
% 3.72/1.37
%------------------------------------------------------------------------------