%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET351+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 : 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 02:47:08 PM UTC 2026
% Result : Theorem 0.63s 1.64s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 12 unt; 0 def)
% Number of atoms : 123 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 54 ~; 51 |; 12 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 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 : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 76 !; 5 ?; 23 :)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
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,conjecture,
! [X0] : equal_set(sum(singleton(X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI39) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(sum(singleton(X0)),X0),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0] : ~ equal_set(sum(singleton(X0)),X0),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
~ equal_set(sum(singleton(sK0)),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ member(X0,singleton(X1))
| X0 = X1 )
& ( X0 != X1
| member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f22,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(f23,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,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f23]) ).
fof(f25,plain,
! [X0,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))],[f19]) ).
fof(f26,plain,
~ equal_set(sum(singleton(sK0)),sK0),
inference(cnf_transformation,[],[f20]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(X0,sK1(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f31,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f29]) ).
tcf(c_49,negated_conjecture,
~ equal_set(sum(singleton(sK0)),sK0),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i] : member(X0,singleton(X0)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,sum(X2))
| ~ member(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( member(X0,sK1(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_58,plain,
member(sK0,singleton(sK0)),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( X1 != sK0 )
| ( sum(singleton(sK0)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_50]) ).
tcf(c_140,plain,
( ~ subset(sK0,sum(singleton(sK0)))
| ~ subset(sum(singleton(sK0)),sK0) ),
inference(unflattening,[status(thm)],[c_139]) ).
tcf(c_453,plain,
( subset(sum(singleton(sK0)),sK0)
| ~ member(sK2(sum(singleton(sK0)),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_454,plain,
( subset(sum(singleton(sK0)),sK0)
| member(sK2(sum(singleton(sK0)),sK0),sum(singleton(sK0))) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_476,plain,
( subset(sK0,sum(singleton(sK0)))
| member(sK2(sK0,sum(singleton(sK0))),sK0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_477,plain,
( subset(sK0,sum(singleton(sK0)))
| ~ member(sK2(sK0,sum(singleton(sK0))),sum(singleton(sK0))) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i] :
( ( sK1(X0,singleton(X1)) = X1 )
| ~ member(X0,sum(singleton(X1))) ),
inference(superposition,[status(thm)],[c_54,c_52]) ).
tcf(c_594,plain,
! [X0: $i] :
( member(sK2(sK0,sum(singleton(sK0))),sum(X0))
| ~ member(sK0,X0)
| ~ member(sK2(sK0,sum(singleton(sK0))),sK0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_887,plain,
( member(sK2(sK0,sum(singleton(sK0))),sum(singleton(sK0)))
| ~ member(sK0,singleton(sK0))
| ~ member(sK2(sK0,sum(singleton(sK0))),sK0) ),
inference(instantiation,[status(thm)],[c_594]) ).
tcf(c_1507,plain,
! [X0: $i,X1: $i] :
( subset(sum(singleton(X0)),X1)
| ( sK1(sK2(sum(singleton(X0)),X1),singleton(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_57,c_554]) ).
tcf(c_2623,plain,
~ subset(sum(singleton(sK0)),sK0),
inference(global_subsumption_just,[status(thm)],[c_140,c_58,c_140,c_477,c_476,c_887]) ).
tcf(c_2846,plain,
sK1(sK2(sum(singleton(sK0)),sK0),singleton(sK0)) = sK0,
inference(superposition,[status(thm)],[c_1507,c_2623]) ).
tcf(c_3314,plain,
( member(sK2(sum(singleton(sK0)),sK0),sK0)
| ~ member(sK2(sum(singleton(sK0)),sK0),sum(singleton(sK0))) ),
inference(superposition,[status(thm)],[c_2846,c_55]) ).
tcf(c_3318,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3314,c_2623,c_454,c_453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.20/0.66 % Computer : n020.cluster.edu
% 0.20/0.66 % Model : x86_64 x86_64
% 0.20/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.66 % Memory : 8046.5625MB
% 0.20/0.66 % OS : Linux 6.8.0-71-generic
% 0.20/0.66 % CPULimit : 300
% 0.20/0.66 % WCLimit : 300
% 0.20/0.66 % DateTime : Thu Sep 24 10:41:20 UTC 2026
% 0.20/0.66 % CPUTime :
% 0.20/0.66 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.72 Running first-order theorem proving
% 0.23/0.72 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
% 0.23/0.74
% 0.23/0.74 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.74
% 0.23/0.74 % Detected problem language: tptp
% 0.23/0.76 % Proving...
% 0.63/1.64 % SZS status Started for theBenchmark.p
% 0.63/1.64 % SZS status Theorem for theBenchmark.p
% 0.63/1.64
% 0.63/1.64 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.63/1.64
% 0.63/1.64 % ------ iProver source info
% 0.63/1.64
% 0.63/1.64 % git: date: 2026-07-19 20:42:38 +0200
% 0.63/1.64 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.63/1.64 % git: non_committed_changes: false
% 0.63/1.64
% 0.63/1.64 % ------ Parsing...
% 0.63/1.64 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.63/1.64
% 0.63/1.64 % ------ 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 %
% 0.63/1.64
% 0.63/1.64 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.63/1.64
% 0.63/1.64 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.63/1.64 % ------ Proving...
% 0.63/1.64 % ------ Problem Properties
% 0.63/1.64
% 0.63/1.64 %
% 0.63/1.64 % clauses 8
% 0.63/1.64 % conjectures 0
% 0.63/1.64 % EPR 0
% 0.63/1.64 % Horn 7
% 0.63/1.64 % unary 1
% 0.63/1.64 % binary 6
% 0.63/1.64 % lits 16
% 0.63/1.64 % lits eq 1
% 0.63/1.64 % fd_pure 0
% 0.63/1.64 % fd_pseudo 0
% 0.63/1.64 % fd_cond 0
% 0.63/1.64 % fd_pseudo_cond 1
% 0.63/1.64 % AC symbols 0
% 0.63/1.64
% 0.63/1.64 % ------ Schedule dynamic 5 is on
% 0.63/1.64
% 0.63/1.64 % ------ no conjectures: strip conj schedule
% 0.63/1.64
% 0.63/1.64 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.63/1.64
% 0.63/1.64
% 0.63/1.64 % ------
% 0.63/1.64 % Current options:
% 0.63/1.64 % ------
% 0.63/1.64
% 0.63/1.64
% 0.63/1.64 %
% 0.63/1.64
% 0.63/1.64 % ------ Proving...
% 0.63/1.64 %
% 0.63/1.64
% 0.63/1.64 % SZS status Theorem for theBenchmark.p
% 0.63/1.64
% 0.63/1.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.63/1.64
% 0.63/1.64
%------------------------------------------------------------------------------