%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU145+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 : 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 02:55:35 PM UTC 2026
% Result : Theorem 5.66s 1.75s
% Output : CNFRefutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 18 unt; 2 def)
% Number of atoms : 243 ( 45 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 245 ( 93 ~; 101 |; 42 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 119 ( 0 sgn 106 !; 13 ?; 28 :)
% 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(f4,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& ~ subset(X0,set_difference(X1,singleton(X2)))
& ~ in(X2,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& ~ subset(X0,set_difference(X1,singleton(X2)))
& ~ in(X2,X0) ),
inference(flattening,[],[f13]) ).
fof(f15,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(f16,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,[],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,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,[],[f12]) ).
fof(f19,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,[],[f18]) ).
fof(f20,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))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| ( ~ in(sK2(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f23]) ).
fof(f25,plain,
( subset(sK3,sK4)
& ~ subset(sK3,set_difference(sK4,singleton(sK5)))
& ~ in(sK5,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f14]) ).
fof(f27,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
~ subset(sK3,set_difference(sK4,singleton(sK5))),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
~ in(sK5,sK3),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f28]) ).
fof(f45,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f44]) ).
fof(f46,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f27]) ).
fof(f47,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f36]) ).
tcf(c_52,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,negated_conjecture,
~ in(sK5,sK3),
inference(cnf_transformation,[],[f42]) ).
tcf(c_64,negated_conjecture,
~ subset(sK3,set_difference(sK4,singleton(sK5))),
inference(cnf_transformation,[],[f41]) ).
tcf(c_65,negated_conjecture,
subset(sK3,sK4),
inference(cnf_transformation,[],[f40]) ).
tcf(c_291,definition,
iPr_def_10 = singleton(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_292,definition,
iPr_def_11 = set_difference(sK4,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_293,negated_conjecture,
subset(sK3,sK4),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_294,negated_conjecture,
~ subset(sK3,iPr_def_11),
inference(demodulation,[status(thm)],[c_64,c_291,c_292]) ).
tcf(c_295,negated_conjecture,
~ in(sK5,sK3),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_559,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ( sK1(singleton(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_55,c_53]) ).
tcf(c_560,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_291,c_53]) ).
tcf(c_685,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_52,c_56]) ).
tcf(c_686,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK1(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_707,plain,
( subset(sK3,iPr_def_11)
| ~ in(sK1(sK3,iPr_def_11),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_715,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| in(X0,iPr_def_10)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_292,c_60]) ).
tcf(c_950,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( sK1(singleton(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_559,c_685]) ).
tcf(c_1196,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( sK1(singleton(sK1(X0,X1)),X1) = sK1(X0,X1) ) ),
inference(superposition,[status(thm)],[c_950,c_54]) ).
tcf(c_1622,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),iPr_def_11)
| in(sK1(X0,X1),iPr_def_10)
| ~ subset(X0,sK4) ),
inference(superposition,[status(thm)],[c_686,c_715]) ).
tcf(c_11620,plain,
sK1(singleton(sK1(sK3,iPr_def_11)),iPr_def_11) = sK1(sK3,iPr_def_11),
inference(superposition,[status(thm)],[c_1196,c_294]) ).
tcf(c_11864,plain,
( subset(singleton(sK1(sK3,iPr_def_11)),iPr_def_11)
| ~ in(sK1(sK3,iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_11620,c_54]) ).
tcf(c_11949,plain,
~ in(sK1(sK3,iPr_def_11),iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_11864,c_294,c_707]) ).
tcf(c_13205,plain,
( subset(sK3,iPr_def_11)
| in(sK1(sK3,iPr_def_11),iPr_def_10)
| ~ subset(sK3,sK4) ),
inference(superposition,[status(thm)],[c_1622,c_11949]) ).
tcf(c_13208,plain,
in(sK1(sK3,iPr_def_11),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_13205,c_294,c_293]) ).
tcf(c_13754,plain,
sK1(sK3,iPr_def_11) = sK5,
inference(superposition,[status(thm)],[c_13208,c_560]) ).
tcf(c_13835,plain,
( subset(sK3,iPr_def_11)
| in(sK5,sK3) ),
inference(superposition,[status(thm)],[c_13754,c_55]) ).
tcf(c_13840,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13835,c_294,c_295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU145+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:57:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 5.66/1.75 % SZS status Started for theBenchmark.p
% 5.66/1.75 % SZS status Theorem for theBenchmark.p
% 5.66/1.75
% 5.66/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.66/1.75
% 5.66/1.75 % ------ iProver source info
% 5.66/1.75
% 5.66/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 5.66/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.66/1.75 % git: non_committed_changes: false
% 5.66/1.75
% 5.66/1.75 % ------ Parsing...
% 5.66/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.66/1.75
% 5.66/1.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 5.66/1.75
% 5.66/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.66/1.75
% 5.66/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.66/1.75 % ------ Proving...
% 5.66/1.75 % ------ Problem Properties
% 5.66/1.75
% 5.66/1.75 %
% 5.66/1.75 % clauses 20
% 5.66/1.75 % conjectures 3
% 5.66/1.75 % EPR 6
% 5.66/1.75 % Horn 14
% 5.66/1.75 % unary 7
% 5.66/1.75 % binary 6
% 5.66/1.75 % lits 41
% 5.66/1.75 % lits eq 10
% 5.66/1.75 % fd_pure 0
% 5.66/1.75 % fd_pseudo 0
% 5.66/1.75 % fd_cond 0
% 5.66/1.75 % fd_pseudo_cond 5
% 5.66/1.75 % AC symbols 0
% 5.66/1.75
% 5.66/1.75 % ------ Schedule dynamic 5 is on
% 5.66/1.75
% 5.66/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.66/1.75
% 5.66/1.75
% 5.66/1.75 % ------
% 5.66/1.75 % Current options:
% 5.66/1.75 % ------
% 5.66/1.75
% 5.66/1.75
% 5.66/1.75 %
% 5.66/1.75
% 5.66/1.75 % ------ Proving...
% 5.66/1.75 %
% 5.66/1.75
% 5.66/1.75 % SZS status Theorem for theBenchmark.p
% 5.66/1.75
% 5.66/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.66/1.76
% 5.66/1.76
%------------------------------------------------------------------------------