%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU135+1 : 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 02:55:32 PM UTC 2026
% Result : Theorem 7.27s 1.75s
% Output : CNFRefutation 7.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 218 ( 38 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 271 ( 102 ~; 124 |; 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 : 123 ( 0 sgn 115 !; 8 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f6,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(f18,conjecture,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f31,plain,
? [X0,X1] : set_union2(X0,X1) != set_union2(X0,set_difference(X1,X0)),
inference(ennf_transformation,[],[f19]) ).
fof(f37,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,[],[f4]) ).
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(flattening,[],[f37]) ).
fof(f39,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,[],[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) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ( ~ in(sK0(X0,X1,X2),X1)
& ~ in(sK0(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f39]) ).
fof(f44,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,[],[f6]) ).
fof(f45,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,[],[f44]) ).
fof(f46,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,[],[f45]) ).
fof(f47,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))],[f46]) ).
fof(f50,plain,
set_union2(sK5,sK6) != set_union2(sK5,set_difference(sK6,sK5)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f31]) ).
fof(f56,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f57,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f58,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f59,plain,
! [X2,X0,X1] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f40]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f40]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f40]) ).
fof(f66,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f79,plain,
set_union2(sK5,sK6) != set_union2(sK5,set_difference(sK6,sK5)),
inference(cnf_transformation,[],[f50]) ).
fof(f87,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f58]) ).
fof(f88,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f57]) ).
fof(f89,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f56]) ).
fof(f90,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f67]) ).
fof(f91,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f66]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_77,negated_conjecture,
set_union2(sK5,set_difference(sK6,sK5)) != set_union2(sK5,sK6),
inference(cnf_transformation,[],[f79]) ).
tcf(c_725,plain,
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK5)
| in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_difference(sK6,sK5))
| in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_union2(sK5,sK6))
| ( set_union2(sK5,set_difference(sK6,sK5)) = set_union2(sK5,sK6) ) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_726,plain,
( ( set_union2(sK5,set_difference(sK6,sK5)) = set_union2(sK5,sK6) )
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK5)
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_union2(sK5,sK6)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_727,plain,
( ( set_union2(sK5,set_difference(sK6,sK5)) = set_union2(sK5,sK6) )
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_difference(sK6,sK5))
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_union2(sK5,sK6)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_764,plain,
! [X0: $i] :
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK5)
| in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),X0)
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_union2(sK5,X0)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_769,plain,
! [X0: $i] :
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK5)
| in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_difference(X0,sK5))
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),X0) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_777,plain,
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_union2(sK5,sK6))
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK5) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_778,plain,
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_union2(sK5,sK6))
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK6) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_859,plain,
! [X0: $i] :
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK6)
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_difference(sK6,X0)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1074,plain,
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK6)
| in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK5)
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_union2(sK5,sK6)) ),
inference(instantiation,[status(thm)],[c_764]) ).
tcf(c_2552,plain,
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK5)
| in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_difference(sK6,sK5))
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK6) ),
inference(instantiation,[status(thm)],[c_769]) ).
tcf(c_6764,plain,
( in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),sK6)
| ~ in(sK0(sK5,set_difference(sK6,sK5),set_union2(sK5,sK6)),set_difference(sK6,sK5)) ),
inference(instantiation,[status(thm)],[c_859]) ).
tcf(c_6765,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6764,c_2552,c_1074,c_778,c_777,c_725,c_726,c_727,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU135+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n020.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Thu Sep 24 12:54:03 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.40 Running first-order theorem proving
% 0.17/0.40 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
% 0.17/0.41
% 0.17/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.41
% 0.17/0.41 % Detected problem language: tptp
% 0.17/0.43 % Proving...
% 7.27/1.75 % SZS status Started for theBenchmark.p
% 7.27/1.75 % SZS status Theorem for theBenchmark.p
% 7.27/1.75
% 7.27/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.27/1.75
% 7.27/1.75 % ------ iProver source info
% 7.27/1.75
% 7.27/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 7.27/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.27/1.75 % git: non_committed_changes: false
% 7.27/1.75
% 7.27/1.75 % ------ Parsing...
% 7.27/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.27/1.75
% 7.27/1.75 % ------ 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 %
% 7.27/1.75
% 7.27/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.27/1.75
% 7.27/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.27/1.75 % ------ Proving...
% 7.27/1.75 % ------ Problem Properties
% 7.27/1.75
% 7.27/1.75 %
% 7.27/1.75 % clauses 32
% 7.27/1.75 % conjectures 1
% 7.27/1.75 % EPR 10
% 7.27/1.75 % Horn 25
% 7.27/1.75 % unary 10
% 7.27/1.75 % binary 11
% 7.27/1.75 % lits 67
% 7.27/1.75 % lits eq 15
% 7.27/1.75 % fd_pure 0
% 7.27/1.75 % fd_pseudo 0
% 7.27/1.75 % fd_cond 1
% 7.27/1.75 % fd_pseudo_cond 8
% 7.27/1.75 % AC symbols 0
% 7.27/1.75
% 7.27/1.75 % ------ Input Options Time Limit: Unbounded
% 7.27/1.75
% 7.27/1.75
% 7.27/1.75 % ------
% 7.27/1.75 % Current options:
% 7.27/1.75 % ------
% 7.27/1.75
% 7.27/1.75
% 7.27/1.75 %
% 7.27/1.75
% 7.27/1.75 % ------ Proving...
% 7.27/1.75 %
% 7.27/1.75
% 7.27/1.75 % SZS status Theorem for theBenchmark.p
% 7.27/1.75
% 7.27/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.27/1.75
% 7.27/1.75
%------------------------------------------------------------------------------