%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.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 02:49:07 PM UTC 2026
% Result : Theorem 2.00s 1.30s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 50 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 23 ~; 19 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 20 !; 4 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
fof(f5,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f8,plain,
? [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<~> ~ in(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f11,plain,
? [X0,X1] :
( ( set_difference(singleton(X0),X1) = singleton(X0)
| ~ in(X0,X1) )
& ( singleton(X0) != set_difference(singleton(X0),X1)
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f12,plain,
( ( singleton(sK2) = set_difference(singleton(sK2),sK3)
| ~ in(sK2,sK3) )
& ( singleton(sK2) != set_difference(singleton(sK2),sK3)
| in(sK2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( singleton(X0) != set_difference(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f17,plain,
( singleton(sK2) = set_difference(singleton(sK2),sK3)
| ~ in(sK2,sK3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
( singleton(sK2) != set_difference(singleton(sK2),sK3)
| in(sK2,sK3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( singleton(X0) != set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( in(X0,X1)
| singleton(X0) = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_52,negated_conjecture,
( in(sK2,sK3)
| ( set_difference(singleton(sK2),sK3) != singleton(sK2) ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,negated_conjecture,
( ( set_difference(singleton(sK2),sK3) = singleton(sK2) )
| ~ in(sK2,sK3) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ( set_difference(singleton(X0),X1) != singleton(X0) ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_58,plain,
( ( set_difference(singleton(sK2),sK3) != singleton(sK2) )
| in(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
tcf(c_59,plain,
( in(sK2,sK3)
| ( set_difference(singleton(sK2),sK3) != singleton(sK2) ) ),
inference(renaming,[status(thm)],[c_58]) ).
tcf(c_60,plain,
( ( set_difference(singleton(sK2),sK3) = singleton(sK2) )
| ~ in(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( set_difference(singleton(X0),X1) = singleton(X0) )
| in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(renaming,[status(thm)],[c_64]) ).
tcf(c_96,plain,
in(sK2,sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_59,c_65]) ).
tcf(c_98,plain,
set_difference(singleton(sK2),sK3) = singleton(sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_60,c_65]) ).
tcf(c_375,plain,
~ in(sK2,sK3),
inference(superposition,[status(thm)],[c_98,c_55]) ).
tcf(c_379,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_375,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 12:24:48 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.44
% 0.10/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 2.00/1.30 % SZS status Started for theBenchmark.p
% 2.00/1.30 % SZS status Theorem for theBenchmark.p
% 2.00/1.30
% 2.00/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.00/1.30
% 2.00/1.30 % ------ iProver source info
% 2.00/1.30
% 2.00/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.00/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.00/1.30 % git: non_committed_changes: false
% 2.00/1.30
% 2.00/1.30 % ------ Parsing...
% 2.00/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.00/1.30
% 2.00/1.30 % ------ 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 %
% 2.00/1.30
% 2.00/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.00/1.30
% 2.00/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.00/1.30 % ------ Proving...
% 2.00/1.30 % ------ Problem Properties
% 2.00/1.30
% 2.00/1.30 %
% 2.00/1.30 % clauses 6
% 2.00/1.30 % conjectures 0
% 2.00/1.30 % EPR 3
% 2.00/1.30 % Horn 5
% 2.00/1.30 % unary 3
% 2.00/1.30 % binary 3
% 2.00/1.30 % lits 9
% 2.00/1.30 % lits eq 4
% 2.00/1.30 % fd_pure 0
% 2.00/1.30 % fd_pseudo 0
% 2.00/1.30 % fd_cond 0
% 2.00/1.30 % fd_pseudo_cond 0
% 2.00/1.30 % AC symbols 0
% 2.00/1.30
% 2.00/1.30 % ------ Schedule dynamic 5 is on
% 2.00/1.30
% 2.00/1.30 % ------ no conjectures: strip conj schedule
% 2.00/1.30
% 2.00/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.00/1.30
% 2.00/1.30
% 2.00/1.30 % ------
% 2.00/1.30 % Current options:
% 2.00/1.30 % ------
% 2.00/1.30
% 2.00/1.30
% 2.00/1.30 %
% 2.00/1.30
% 2.00/1.30 % ------ Proving...
% 2.00/1.30 %
% 2.00/1.30
% 2.00/1.30 % SZS status Theorem for theBenchmark.p
% 2.00/1.30
% 2.00/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.00/1.30
% 2.00/1.30
%------------------------------------------------------------------------------