%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET814+4 : TPTP v9.3.1. Released v3.2.0.
% 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 02:48:38 PM UTC 2026
% Result : Theorem 10.20s 2.24s
% Output : CNFRefutation 10.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 5 unt; 0 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 182 ( 70 ~; 68 |; 35 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 68 !; 9 ?; 15 :)
% 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(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( member(X1,X0)
=> subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(f21,conjecture,
! [X0] :
( member(X0,on)
=> subset(sum(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV14) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> subset(sum(X0),X0) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f24,plain,
? [X0] :
( member(X0,on)
& ~ subset(sum(X0),X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( ~ member(X1,X0)
| subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f38,plain,
( member(sK1,on)
& ~ subset(sum(sK1),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f24]) ).
fof(f39,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,[],[f27]) ).
fof(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ? [X2] :
( member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ? [X3] :
( member(X0,X3)
& member(X3,X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(rectify,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ( member(X0,sK3(X0,X1))
& member(sK3(X0,X1),X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f43]) ).
fof(f45,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X1] :
( ~ member(X1,X0)
| subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ? [X1] :
( member(X1,X0)
& ~ subset(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X1] :
( ~ member(X1,X0)
| subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ? [X1] :
( member(X1,X0)
& ~ subset(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X2] :
( ~ member(X2,X0)
| subset(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ? [X1] :
( member(X1,X0)
& ~ subset(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ( ~ member(X0,on)
| ( ! [X2] :
( ~ member(X2,X0)
| subset(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) )
& ( ( member(sK4(X0),X0)
& ~ subset(sK4(X0),X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0)
| member(X0,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f47]) ).
fof(f66,plain,
member(sK1,on),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
~ subset(sum(sK1),sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f69,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f70,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f71,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f72,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(X0,sK3(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f73,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f75,plain,
! [X2,X0] :
( ~ member(X0,on)
| ~ member(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_49,negated_conjecture,
~ subset(sum(sK1),sK1),
inference(cnf_transformation,[],[f67]) ).
tcf(c_50,negated_conjecture,
member(sK1,on),
inference(cnf_transformation,[],[f66]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( member(sK3(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( member(X0,sK3(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(X1,on)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_3412,plain,
( subset(sum(sK1),sK1)
| ~ member(sK2(sum(sK1),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3413,plain,
( subset(sum(sK1),sK1)
| member(sK2(sum(sK1),sK1),sum(sK1)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_3701,plain,
( member(sK2(sum(sK1),sK1),sK3(sK2(sum(sK1),sK1),sK1))
| ~ member(sK2(sum(sK1),sK1),sum(sK1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_3702,plain,
( member(sK3(sK2(sum(sK1),sK1),sK1),sK1)
| ~ member(sK2(sum(sK1),sK1),sum(sK1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_3857,plain,
! [X0: $i] :
( subset(X0,sK1)
| ~ member(sK1,on)
| ~ member(X0,sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_5170,plain,
! [X0: $i] :
( member(sK2(sum(sK1),sK1),X0)
| ~ subset(sK3(sK2(sum(sK1),sK1),sK1),X0)
| ~ member(sK2(sum(sK1),sK1),sK3(sK2(sum(sK1),sK1),sK1)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_5920,plain,
( subset(sK3(sK2(sum(sK1),sK1),sK1),sK1)
| ~ member(sK1,on)
| ~ member(sK3(sK2(sum(sK1),sK1),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_3857]) ).
tcf(c_13981,plain,
( member(sK2(sum(sK1),sK1),sK1)
| ~ subset(sK3(sK2(sum(sK1),sK1),sK1),sK1)
| ~ member(sK2(sum(sK1),sK1),sK3(sK2(sum(sK1),sK1),sK1)) ),
inference(instantiation,[status(thm)],[c_5170]) ).
tcf(c_13982,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13981,c_5920,c_3701,c_3702,c_3413,c_3412,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET814+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:04:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 10.20/2.24 % SZS status Started for theBenchmark.p
% 10.20/2.24 % SZS status Theorem for theBenchmark.p
% 10.20/2.24
% 10.20/2.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.20/2.24
% 10.20/2.24 % ------ iProver source info
% 10.20/2.24
% 10.20/2.24 % git: date: 2026-07-19 20:42:38 +0200
% 10.20/2.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.20/2.24 % git: non_committed_changes: false
% 10.20/2.24
% 10.20/2.24 % ------ Parsing...
% 10.20/2.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.20/2.24
% 10.20/2.24 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.20/2.24
% 10.20/2.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.20/2.24
% 10.20/2.24 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.20/2.24 % ------ Proving...
% 10.20/2.24 % ------ Problem Properties
% 10.20/2.24
% 10.20/2.24 %
% 10.20/2.24 % clauses 42
% 10.20/2.24 % conjectures 2
% 10.20/2.24 % EPR 15
% 10.20/2.24 % Horn 27
% 10.20/2.24 % unary 3
% 10.20/2.24 % binary 18
% 10.20/2.24 % lits 112
% 10.20/2.24 % lits eq 3
% 10.20/2.24 % fd_pure 0
% 10.20/2.24 % fd_pseudo 0
% 10.20/2.24 % fd_cond 0
% 10.20/2.24 % fd_pseudo_cond 2
% 10.20/2.24 % AC symbols 0
% 10.20/2.24
% 10.20/2.24 % ------ Schedule dynamic 5 is on
% 10.20/2.24
% 10.20/2.24 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.20/2.24
% 10.20/2.24
% 10.20/2.24 % ------
% 10.20/2.24 % Current options:
% 10.20/2.24 % ------
% 10.20/2.24
% 10.20/2.24
% 10.20/2.24 %
% 10.20/2.24
% 10.20/2.24 % ------ Proving...
% 10.20/2.24 %
% 10.20/2.24
% 10.20/2.24 % SZS status Theorem for theBenchmark.p
% 10.20/2.24
% 10.20/2.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.20/2.24
% 10.20/2.24
%------------------------------------------------------------------------------