%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU138+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 : n005.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 02:55:33 PM UTC 2026
% Result : Theorem 4.34s 1.28s
% Output : CNFRefutation 4.34s
% 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 : 278 ( 109 ~; 123 |; 42 &)
% ( 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(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_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/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f17,conjecture,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f24,plain,
? [X0,X1] : set_intersection2(X0,X1) != set_difference(X0,set_difference(X0,X1)),
inference(ennf_transformation,[],[f18]) ).
fof(f29,plain,
set_intersection2(sK0,sK1) != set_difference(sK0,set_difference(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f32]) ).
fof(f34,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(f35,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,[],[f34]) ).
fof(f36,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,[],[f35]) ).
fof(f37,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))],[f36]) ).
fof(f40,plain,
set_intersection2(sK0,sK1) != set_difference(sK0,set_difference(sK0,sK1)),
inference(cnf_transformation,[],[f29]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X2,X0,X1] :
( in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),X1)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
! [X2,X0,X1] :
( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f65,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f45]) ).
fof(f66,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f44]) ).
fof(f67,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f43]) ).
fof(f68,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f54]) ).
fof(f70,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f52]) ).
tcf(c_49,negated_conjecture,
set_difference(sK0,set_difference(sK0,sK1)) != set_intersection2(sK0,sK1),
inference(cnf_transformation,[],[f40]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X1)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_864,plain,
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK0)
| in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_intersection2(sK0,sK1))
| ( set_difference(sK0,set_difference(sK0,sK1)) = set_intersection2(sK0,sK1) ) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_865,plain,
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_intersection2(sK0,sK1))
| ( set_difference(sK0,set_difference(sK0,sK1)) = set_intersection2(sK0,sK1) )
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_difference(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_866,plain,
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_difference(sK0,sK1))
| ( set_difference(sK0,set_difference(sK0,sK1)) = set_intersection2(sK0,sK1) )
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK0)
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_intersection2(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_879,plain,
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK1)
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_intersection2(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_880,plain,
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK0)
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_intersection2(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1052,plain,
! [X0: $i] :
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),X0)
| in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_difference(sK0,X0))
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1053,plain,
! [X0: $i] :
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_intersection2(sK0,X0))
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK0)
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1294,plain,
! [X0: $i] :
( ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK1)
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_difference(X0,sK1)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_3626,plain,
( ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK1)
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_difference(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1294]) ).
tcf(c_4491,plain,
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK1)
| in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_difference(sK0,sK1))
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_1052]) ).
tcf(c_4493,plain,
( in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),set_intersection2(sK0,sK1))
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK1)
| ~ in(sK3(sK0,set_difference(sK0,sK1),set_intersection2(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_1053]) ).
tcf(c_4494,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4493,c_4491,c_3626,c_879,c_880,c_866,c_865,c_864,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU138+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:53:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 4.34/1.28 % SZS status Started for theBenchmark.p
% 4.34/1.28 % SZS status Theorem for theBenchmark.p
% 4.34/1.28
% 4.34/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.34/1.28
% 4.34/1.28 % ------ iProver source info
% 4.34/1.28
% 4.34/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.34/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.34/1.28 % git: non_committed_changes: false
% 4.34/1.28
% 4.34/1.28 % ------ Parsing...
% 4.34/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.34/1.28
% 4.34/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.34/1.28
% 4.34/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.34/1.28
% 4.34/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.34/1.28 % ------ Proving...
% 4.34/1.28 % ------ Problem Properties
% 4.34/1.28
% 4.34/1.28 %
% 4.34/1.28 % clauses 25
% 4.34/1.28 % conjectures 1
% 4.34/1.28 % EPR 7
% 4.34/1.28 % Horn 19
% 4.34/1.28 % unary 9
% 4.34/1.28 % binary 7
% 4.34/1.28 % lits 52
% 4.34/1.28 % lits eq 14
% 4.34/1.28 % fd_pure 0
% 4.34/1.28 % fd_pseudo 0
% 4.34/1.28 % fd_cond 1
% 4.34/1.28 % fd_pseudo_cond 7
% 4.34/1.28 % AC symbols 0
% 4.34/1.28
% 4.34/1.28 % ------ Schedule dynamic 5 is on
% 4.34/1.28
% 4.34/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.34/1.28
% 4.34/1.28
% 4.34/1.28 % ------
% 4.34/1.28 % Current options:
% 4.34/1.28 % ------
% 4.34/1.28
% 4.34/1.28
% 4.34/1.28 %
% 4.34/1.28
% 4.34/1.28 % ------ Proving...
% 4.34/1.28 %
% 4.34/1.28
% 4.34/1.28 % SZS status Theorem for theBenchmark.p
% 4.34/1.28
% 4.34/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.34/1.28
% 4.34/1.28
%------------------------------------------------------------------------------