%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU137+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 : n007.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 02:55:32 PM UTC 2026
% Result : Theorem 2.38s 1.18s
% Output : CNFRefutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 5 unt; 0 def)
% Number of atoms : 211 ( 37 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 262 ( 96 ~; 113 |; 43 &)
% ( 5 <=>; 5 =>; 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; 2 con; 0-3 aty)
% Number of variables : 110 ( 0 sgn 102 !; 8 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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(f19,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> X1 = set_union2(X0,set_difference(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> X1 = set_union2(X0,set_difference(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f28,plain,
? [X0,X1] :
( subset(X0,X1)
& set_union2(X0,set_difference(X1,X0)) != X1 ),
inference(ennf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f37,plain,
( subset(sK0,sK1)
& sK1 != set_union2(sK0,set_difference(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f28]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f40]) ).
fof(f42,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,[],[f5]) ).
fof(f43,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,[],[f42]) ).
fof(f44,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,[],[f43]) ).
fof(f45,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(sK3(X0,X1,X2),X2)
| ( ~ in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f44]) ).
fof(f50,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f51,plain,
sK1 != set_union2(sK0,set_difference(sK1,sK0)),
inference(cnf_transformation,[],[f37]) ).
fof(f60,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f68,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f85,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f68]) ).
fof(f86,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f67]) ).
tcf(c_49,negated_conjecture,
set_union2(sK0,set_difference(sK1,sK0)) != sK1,
inference(cnf_transformation,[],[f51]) ).
tcf(c_50,negated_conjecture,
subset(sK0,sK1),
inference(cnf_transformation,[],[f50]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ~ in(X2,X1)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_72]) ).
tcf(c_345,plain,
! [X0: $i] :
( in(X0,sK1)
| ~ in(X0,sK0) ),
inference(unflattening,[status(thm)],[c_344]) ).
tcf(c_1244,plain,
( ( set_union2(sK0,set_difference(sK1,sK0)) = sK1 )
| ~ in(sK2(sK0,set_difference(sK1,sK0),sK1),sK0)
| ~ in(sK2(sK0,set_difference(sK1,sK0),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1255,plain,
( ( set_union2(sK0,set_difference(sK1,sK0)) = sK1 )
| ~ in(sK2(sK0,set_difference(sK1,sK0),sK1),sK1)
| ~ in(sK2(sK0,set_difference(sK1,sK0),sK1),set_difference(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1312,plain,
( in(sK2(sK0,set_difference(sK1,sK0),sK1),sK0)
| in(sK2(sK0,set_difference(sK1,sK0),sK1),sK1)
| in(sK2(sK0,set_difference(sK1,sK0),sK1),set_difference(sK1,sK0))
| ( set_union2(sK0,set_difference(sK1,sK0)) = sK1 ) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1455,plain,
! [X0: $i] :
( in(sK2(sK0,set_difference(sK1,sK0),sK1),X0)
| in(sK2(sK0,set_difference(sK1,sK0),sK1),set_difference(sK1,X0))
| ~ in(sK2(sK0,set_difference(sK1,sK0),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1907,plain,
( in(sK2(sK0,set_difference(sK1,sK0),sK1),sK1)
| ~ in(sK2(sK0,set_difference(sK1,sK0),sK1),sK0) ),
inference(instantiation,[status(thm)],[c_345]) ).
tcf(c_3143,plain,
( in(sK2(sK0,set_difference(sK1,sK0),sK1),sK1)
| ~ in(sK2(sK0,set_difference(sK1,sK0),sK1),set_difference(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_5927,plain,
( in(sK2(sK0,set_difference(sK1,sK0),sK1),sK0)
| in(sK2(sK0,set_difference(sK1,sK0),sK1),set_difference(sK1,sK0))
| ~ in(sK2(sK0,set_difference(sK1,sK0),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_1455]) ).
tcf(c_5928,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5927,c_3143,c_1907,c_1312,c_1255,c_1244,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU137+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:51:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.38/1.18 % SZS status Started for theBenchmark.p
% 2.38/1.18 % SZS status Theorem for theBenchmark.p
% 2.38/1.18
% 2.38/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.38/1.18
% 2.38/1.18 % ------ iProver source info
% 2.38/1.18
% 2.38/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.38/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.38/1.18 % git: non_committed_changes: false
% 2.38/1.18
% 2.38/1.18 % ------ Parsing...
% 2.38/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.38/1.18
% 2.38/1.18 % ------ 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 %
% 2.38/1.18
% 2.38/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.38/1.18
% 2.38/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.38/1.18 % ------ Proving...
% 2.38/1.18 % ------ Problem Properties
% 2.38/1.18
% 2.38/1.18 %
% 2.38/1.18 % clauses 30
% 2.38/1.18 % conjectures 1
% 2.38/1.18 % EPR 8
% 2.38/1.18 % Horn 23
% 2.38/1.18 % unary 9
% 2.38/1.18 % binary 10
% 2.38/1.18 % lits 64
% 2.38/1.18 % lits eq 16
% 2.38/1.18 % fd_pure 0
% 2.38/1.18 % fd_pseudo 0
% 2.38/1.18 % fd_cond 1
% 2.38/1.18 % fd_pseudo_cond 9
% 2.38/1.18 % AC symbols 0
% 2.38/1.18
% 2.38/1.18 % ------ Schedule dynamic 5 is on
% 2.38/1.18
% 2.38/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.38/1.18
% 2.38/1.18
% 2.38/1.18 % ------
% 2.38/1.18 % Current options:
% 2.38/1.18 % ------
% 2.38/1.18
% 2.38/1.18
% 2.38/1.18 %
% 2.38/1.18
% 2.38/1.18 % ------ Proving...
% 2.38/1.18 %
% 2.38/1.18
% 2.38/1.18 % SZS status Theorem for theBenchmark.p
% 2.38/1.18
% 2.38/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.38/1.19
% 2.38/1.19
%------------------------------------------------------------------------------