%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:55:34 PM UTC 2026
% Result : Theorem 1.93s 1.27s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 7 unt; 0 def)
% Number of atoms : 134 ( 31 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 147 ( 58 ~; 64 |; 17 &)
% ( 6 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 65 !; 8 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
? [X0,X1] :
( subset(singleton(X0),X1)
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f16]) ).
fof(f18,plain,
? [X0,X1] :
( ( subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ subset(singleton(X0),X1)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f19,plain,
( ( subset(singleton(sK2),sK3)
| in(sK2,sK3) )
& ( ~ subset(singleton(sK2),sK3)
| ~ in(sK2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f18]) ).
fof(f21,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
( subset(singleton(sK2),sK3)
| in(sK2,sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
( ~ subset(singleton(sK2),sK3)
| ~ in(sK2,sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f22]) ).
fof(f32,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f31]) ).
fof(f33,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_57,negated_conjecture,
( ~ in(sK2,sK3)
| ~ subset(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_58,negated_conjecture,
( in(sK2,sK3)
| subset(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_61,plain,
in(sK2,singleton(sK2)),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_66,plain,
( ~ subset(singleton(sK2),sK3)
| ~ in(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_67,plain,
( ~ in(sK2,sK3)
| ~ subset(singleton(sK2),sK3) ),
inference(renaming,[status(thm)],[c_66]) ).
tcf(c_68,plain,
( subset(singleton(sK2),sK3)
| in(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_69,plain,
( in(sK2,sK3)
| subset(singleton(sK2),sK3) ),
inference(renaming,[status(thm)],[c_68]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2,sK3)
| in(X2,X1)
| ~ in(X2,X0)
| ( X1 != sK3 )
| ( singleton(sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_69]) ).
tcf(c_240,plain,
! [X0: $i] :
( in(sK2,sK3)
| in(X0,sK3)
| ~ in(X0,singleton(sK2)) ),
inference(unflattening,[status(thm)],[c_239]) ).
tcf(c_241,plain,
( in(sK2,sK3)
| ~ in(sK2,singleton(sK2)) ),
inference(instantiation,[status(thm)],[c_240]) ).
tcf(c_242,plain,
in(sK2,sK3),
inference(global_subsumption_just,[status(thm)],[c_240,c_61,c_241]) ).
tcf(c_265,plain,
~ subset(singleton(sK2),sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_67,c_242]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ( sK1(singleton(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_55,c_53]) ).
tcf(c_551,plain,
sK1(singleton(sK2),sK3) = sK2,
inference(superposition,[status(thm)],[c_489,c_265]) ).
tcf(c_556,plain,
( subset(singleton(sK2),sK3)
| ~ in(sK2,sK3) ),
inference(superposition,[status(thm)],[c_551,c_54]) ).
tcf(c_559,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_556,c_265,c_242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:56:54 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 1.93/1.27 % SZS status Started for theBenchmark.p
% 1.93/1.27 % SZS status Theorem for theBenchmark.p
% 1.93/1.27
% 1.93/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.93/1.27
% 1.93/1.27 % ------ iProver source info
% 1.93/1.27
% 1.93/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.93/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.93/1.27 % git: non_committed_changes: false
% 1.93/1.27
% 1.93/1.27 % ------ Parsing...
% 1.93/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.93/1.27
% 1.93/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.93/1.27
% 1.93/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.93/1.27
% 1.93/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.93/1.27 % ------ Proving...
% 1.93/1.27 % ------ Problem Properties
% 1.93/1.27
% 1.93/1.27 %
% 1.93/1.27 % clauses 11
% 1.93/1.27 % conjectures 0
% 1.93/1.27 % EPR 4
% 1.93/1.27 % Horn 9
% 1.93/1.27 % unary 4
% 1.93/1.27 % binary 4
% 1.93/1.27 % lits 21
% 1.93/1.27 % lits eq 5
% 1.93/1.27 % fd_pure 0
% 1.93/1.27 % fd_pseudo 0
% 1.93/1.27 % fd_cond 0
% 1.93/1.27 % fd_pseudo_cond 2
% 1.93/1.27 % AC symbols 0
% 1.93/1.27
% 1.93/1.27 % ------ Schedule dynamic 5 is on
% 1.93/1.27
% 1.93/1.27 % ------ no conjectures: strip conj schedule
% 1.93/1.27
% 1.93/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.93/1.27
% 1.93/1.27
% 1.93/1.27 % ------
% 1.93/1.27 % Current options:
% 1.93/1.27 % ------
% 1.93/1.27
% 1.93/1.27
% 1.93/1.27 %
% 1.93/1.27
% 1.93/1.27 % ------ Proving...
% 1.93/1.27 %
% 1.93/1.27
% 1.93/1.27 % SZS status Theorem for theBenchmark.p
% 1.93/1.27
% 1.93/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.93/1.27
% 1.93/1.27
%------------------------------------------------------------------------------