%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET925+1 : 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 : n017.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 1.65s 1.27s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 4 unt; 0 def)
% Number of atoms : 52 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 22 ~; 20 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 20 !; 4 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f9,plain,
? [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0,X1] :
( ( set_difference(singleton(X0),X1) = empty_set
| in(X0,X1) )
& ( empty_set != set_difference(singleton(X0),X1)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f13,plain,
( ( empty_set = set_difference(singleton(sK2),sK3)
| in(sK2,sK3) )
& ( empty_set != set_difference(singleton(sK2),sK3)
| ~ in(sK2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( empty_set != set_difference(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f19,plain,
( empty_set = set_difference(singleton(sK2),sK3)
| in(sK2,sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
( empty_set != set_difference(singleton(sK2),sK3)
| ~ in(sK2,sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( empty_set != set_difference(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( ~ in(X0,X1)
| empty_set = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_53,negated_conjecture,
( ~ in(sK2,sK3)
| ( set_difference(singleton(sK2),sK3) != empty_set ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_54,negated_conjecture,
( in(sK2,sK3)
| ( set_difference(singleton(sK2),sK3) = empty_set ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( set_difference(singleton(X0),X1) = empty_set )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(singleton(X0),X1) != empty_set ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_59,plain,
( ( set_difference(singleton(sK2),sK3) != empty_set )
| ~ in(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
tcf(c_60,plain,
( ~ in(sK2,sK3)
| ( set_difference(singleton(sK2),sK3) != empty_set ) ),
inference(renaming,[status(thm)],[c_59]) ).
tcf(c_61,plain,
( ( set_difference(singleton(sK2),sK3) = empty_set )
| in(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_62,plain,
( in(sK2,sK3)
| ( set_difference(singleton(sK2),sK3) = empty_set ) ),
inference(renaming,[status(thm)],[c_61]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( set_difference(singleton(X0),X1) != empty_set )
| in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(singleton(X0),X1) != empty_set ) ),
inference(renaming,[status(thm)],[c_63]) ).
tcf(c_99,plain,
in(sK2,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_62,c_64]) ).
tcf(c_103,plain,
set_difference(singleton(sK2),sK3) != empty_set,
inference(backward_subsumption_resolution,[status(thm)],[c_60,c_99]) ).
tcf(c_340,plain,
set_difference(singleton(sK2),sK3) = empty_set,
inference(superposition,[status(thm)],[c_99,c_55]) ).
tcf(c_341,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_340,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET925+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:18:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.65/1.27 % SZS status Started for theBenchmark.p
% 1.65/1.27 % SZS status Theorem for theBenchmark.p
% 1.65/1.27
% 1.65/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.65/1.27
% 1.65/1.27 % ------ iProver source info
% 1.65/1.27
% 1.65/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.65/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.65/1.27 % git: non_committed_changes: false
% 1.65/1.27
% 1.65/1.27 % ------ Parsing...
% 1.65/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.65/1.27
% 1.65/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.65/1.27
% 1.65/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.65/1.27
% 1.65/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.65/1.27 % ------ Proving...
% 1.65/1.27 % ------ Problem Properties
% 1.65/1.27
% 1.65/1.27 %
% 1.65/1.27 % clauses 8
% 1.65/1.27 % conjectures 0
% 1.65/1.27 % EPR 5
% 1.65/1.27 % Horn 8
% 1.65/1.27 % unary 5
% 1.65/1.27 % binary 3
% 1.65/1.27 % lits 11
% 1.65/1.27 % lits eq 3
% 1.65/1.27 % fd_pure 0
% 1.65/1.27 % fd_pseudo 0
% 1.65/1.27 % fd_cond 0
% 1.65/1.27 % fd_pseudo_cond 0
% 1.65/1.27 % AC symbols 0
% 1.65/1.27
% 1.65/1.27 % ------ Schedule dynamic 5 is on
% 1.65/1.27
% 1.65/1.27 % ------ no conjectures: strip conj schedule
% 1.65/1.27
% 1.65/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.65/1.27
% 1.65/1.27
% 1.65/1.27 % ------
% 1.65/1.27 % Current options:
% 1.65/1.27 % ------
% 1.65/1.27
% 1.65/1.27
% 1.65/1.27 %
% 1.65/1.27
% 1.65/1.27 % ------ Proving...
% 1.65/1.27 %
% 1.65/1.27
% 1.65/1.27 % SZS status Theorem for theBenchmark.p
% 1.65/1.27
% 1.65/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.65/1.27
% 1.65/1.27
%------------------------------------------------------------------------------