%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU132+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:55:31 PM UTC 2026
% Result : Theorem 27.78s 11.91s
% Output : CNFRefutation 27.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 5 unt; 0 def)
% Number of atoms : 152 ( 12 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 185 ( 74 ~; 75 |; 29 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 94 ( 0 sgn 86 !; 8 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f65,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& ~ subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(ennf_transformation,[],[f36]) ).
fof(f83,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,[],[f53]) ).
fof(f84,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,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK2(X0,X1),X0)
& ~ in(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f84]) ).
fof(f90,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,[],[f9]) ).
fof(f91,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,[],[f90]) ).
fof(f92,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,[],[f91]) ).
fof(f93,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(sK4(X0,X1,X2),X2)
| ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) ) )
& ( ~ in(sK4(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f92]) ).
fof(f100,plain,
( subset(sK8,sK9)
& ~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f65]) ).
fof(f117,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f118,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f119,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f127,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f156,plain,
subset(sK8,sK9),
inference(cnf_transformation,[],[f100]) ).
fof(f157,plain,
~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10)),
inference(cnf_transformation,[],[f100]) ).
fof(f180,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f128]) ).
fof(f181,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f127]) ).
fof(f182,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f126]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_102,negated_conjecture,
~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10)),
inference(cnf_transformation,[],[f157]) ).
tcf(c_103,negated_conjecture,
subset(sK8,sK9),
inference(cnf_transformation,[],[f156]) ).
tcf(c_1058,plain,
( subset(set_difference(sK8,sK10),set_difference(sK9,sK10))
| ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1059,plain,
( subset(set_difference(sK8,sK10),set_difference(sK9,sK10))
| in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK8,sK10)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1075,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK10)
| ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK8,sK10)) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_1089,plain,
( in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK10)
| in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10))
| ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_1638,plain,
! [X0: $i] :
( in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9)
| ~ subset(X0,sK9)
| ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),X0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_6189,plain,
( in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK8)
| ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK8,sK10)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_32069,plain,
( in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9)
| ~ subset(sK8,sK9)
| ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK8) ),
inference(instantiation,[status(thm)],[c_1638]) ).
tcf(c_32074,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_32069,c_6189,c_1089,c_1075,c_1058,c_1059,c_102,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU132+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n020.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 12:53:40 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 27.78/11.91 % SZS status Started for theBenchmark.p
% 27.78/11.91 % SZS status Theorem for theBenchmark.p
% 27.78/11.91
% 27.78/11.91 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.78/11.91
% 27.78/11.91 % ------ iProver source info
% 27.78/11.91
% 27.78/11.91 % git: date: 2026-07-19 20:42:38 +0200
% 27.78/11.91 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.78/11.91 % git: non_committed_changes: false
% 27.78/11.91
% 27.78/11.91 % ------ Parsing...
% 27.78/11.91 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.78/11.91
% 27.78/11.91 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e sf_s rm: 1 0s sf_e pe_s pe_e %
% 27.78/11.91
% 27.78/11.91 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 27.78/11.91
% 27.78/11.91 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.78/11.91 % ------ Proving...
% 27.78/11.91 % ------ Problem Properties
% 27.78/11.91
% 27.78/11.91 %
% 27.78/11.91 % clauses 66
% 27.78/11.91 % conjectures 2
% 27.78/11.91 % EPR 17
% 27.78/11.91 % Horn 52
% 27.78/11.91 % unary 18
% 27.78/11.91 % binary 27
% 27.78/11.91 % lits 138
% 27.78/11.91 % lits eq 30
% 27.78/11.91 % fd_pure 0
% 27.78/11.91 % fd_pseudo 0
% 27.78/11.91 % fd_cond 3
% 27.78/11.91 % fd_pseudo_cond 13
% 27.78/11.91 % AC symbols 0
% 27.78/11.91
% 27.78/11.91 % ------ Input Options Time Limit: Unbounded
% 27.78/11.91
% 27.78/11.91
% 27.78/11.91 % ------
% 27.78/11.91 % Current options:
% 27.78/11.91 % ------
% 27.78/11.91
% 27.78/11.91
% 27.78/11.91 %
% 27.78/11.91
% 27.78/11.91 % ------ Proving...
% 27.78/11.91 %
% 27.78/11.91
% 27.78/11.91 % SZS status Theorem for theBenchmark.p
% 27.78/11.91
% 27.78/11.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.78/11.92
% 27.78/11.92
%------------------------------------------------------------------------------