%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU135+2 : 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 : n003.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 18.54s 3.29s
% Output : CNFRefutation 18.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 9 unt; 0 def)
% Number of atoms : 219 ( 39 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 266 ( 99 ~; 122 |; 41 &)
% ( 4 <=>; 0 =>; 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 121 ( 0 sgn 113 !; 8 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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(f9,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(f38,conjecture,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f39,negated_conjecture,
~ ! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f69,plain,
? [X0,X1] : set_union2(X0,X1) != set_union2(X0,set_difference(X1,X0)),
inference(ennf_transformation,[],[f39]) ).
fof(f83,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,[],[f6]) ).
fof(f84,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,[],[f83]) ).
fof(f85,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,[],[f84]) ).
fof(f86,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(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f85]) ).
fof(f94,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(f95,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,[],[f94]) ).
fof(f96,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,[],[f95]) ).
fof(f97,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))],[f96]) ).
fof(f105,plain,
set_union2(sK8,sK9) != set_union2(sK8,set_difference(sK9,sK8)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f69]) ).
fof(f116,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f117,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f118,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f119,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f132,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f133,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f165,plain,
set_union2(sK8,sK9) != set_union2(sK8,set_difference(sK9,sK8)),
inference(cnf_transformation,[],[f105]) ).
fof(f182,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f118]) ).
fof(f183,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f117]) ).
fof(f184,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f116]) ).
fof(f188,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f133]) ).
fof(f189,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f132]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f184]) ).
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,[],[f188]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_106,negated_conjecture,
set_union2(sK8,set_difference(sK9,sK8)) != set_union2(sK8,sK9),
inference(cnf_transformation,[],[f165]) ).
tcf(c_2225,plain,
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9))
| ( set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,sK9) ) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_2226,plain,
( ( set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,sK9) )
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8)
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_2227,plain,
( ( set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,sK9) )
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8))
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_3125,plain,
! [X0: $i] :
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,X0))
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_4314,plain,
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9))
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8) ),
inference(instantiation,[status(thm)],[c_3125]) ).
tcf(c_37916,plain,
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9)) ),
inference(resolution,[status(thm)],[c_59,c_106]) ).
tcf(c_39933,plain,
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8)) ),
inference(global_subsumption_just,[status(thm)],[c_37916,c_106,c_2225,c_4314]) ).
tcf(c_39934,plain,
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9)) ),
inference(renaming,[status(thm)],[c_39933]) ).
tcf(c_39945,plain,
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9)) ),
inference(resolution,[status(thm)],[c_39934,c_76]) ).
tcf(c_40168,plain,
in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9)),
inference(forward_subsumption_resolution,[status(thm)],[c_39945,c_61]) ).
tcf(c_40181,plain,
( ( set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,sK9) )
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8)) ),
inference(resolution,[status(thm)],[c_40168,c_58]) ).
tcf(c_40182,plain,
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8) ),
inference(resolution,[status(thm)],[c_40168,c_62]) ).
tcf(c_40445,plain,
~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8)),
inference(global_subsumption_just,[status(thm)],[c_40181,c_106,c_2227,c_40168]) ).
tcf(c_40452,plain,
( in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8)
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9) ),
inference(resolution,[status(thm)],[c_40445,c_75]) ).
tcf(c_40453,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_40452,c_40182,c_40168,c_2226,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU135+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 12:54:50 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 18.54/3.29 % SZS status Started for theBenchmark.p
% 18.54/3.29 % SZS status Theorem for theBenchmark.p
% 18.54/3.29
% 18.54/3.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.54/3.29
% 18.54/3.29 % ------ iProver source info
% 18.54/3.29
% 18.54/3.29 % git: date: 2026-07-19 20:42:38 +0200
% 18.54/3.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.54/3.29 % git: non_committed_changes: false
% 18.54/3.29
% 18.54/3.29 % ------ Parsing...
% 18.54/3.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.54/3.29
% 18.54/3.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 18.54/3.29
% 18.54/3.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.54/3.29
% 18.54/3.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.54/3.29 % ------ Proving...
% 18.54/3.29 % ------ Problem Properties
% 18.54/3.29
% 18.54/3.29 %
% 18.54/3.29 % clauses 67
% 18.54/3.29 % conjectures 1
% 18.54/3.29 % EPR 16
% 18.54/3.29 % Horn 53
% 18.54/3.29 % unary 18
% 18.54/3.29 % binary 28
% 18.54/3.29 % lits 140
% 18.54/3.29 % lits eq 31
% 18.54/3.29 % fd_pure 0
% 18.54/3.29 % fd_pseudo 0
% 18.54/3.29 % fd_cond 3
% 18.54/3.29 % fd_pseudo_cond 13
% 18.54/3.29 % AC symbols 0
% 18.54/3.29
% 18.54/3.29 % ------ Input Options Time Limit: Unbounded
% 18.54/3.29
% 18.54/3.29
% 18.54/3.29 % ------
% 18.54/3.29 % Current options:
% 18.54/3.29 % ------
% 18.54/3.29
% 18.54/3.29
% 18.54/3.29 %
% 18.54/3.29
% 18.54/3.29 % ------ Proving...
% 18.54/3.29 %
% 18.54/3.29
% 18.54/3.29 % SZS status Theorem for theBenchmark.p
% 18.54/3.29
% 18.54/3.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.54/3.29
% 18.54/3.29
%------------------------------------------------------------------------------