%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU172+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 : n011.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 02:55:45 PM UTC 2026
% Result : Theorem 0.91s 1.29s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 100 ( 15 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 116 ( 43 ~; 39 |; 29 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn 44 !; 9 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,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,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f96,conjecture,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f97,negated_conjecture,
~ ! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f155,plain,
? [X0,X1,X2] :
( element(X2,powerset(X0))
& in(X1,X2)
& in(X1,subset_complement(X0,X2)) ),
inference(ennf_transformation,[],[f97]) ).
fof(f156,plain,
? [X0,X1,X2] :
( element(X2,powerset(X0))
& in(X1,X2)
& in(X1,subset_complement(X0,X2)) ),
inference(flattening,[],[f155]) ).
fof(f179,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f203,plain,
( element(sK5,powerset(sK3))
& in(sK4,sK5)
& in(sK4,subset_complement(sK3,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f156]) ).
fof(f224,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,[],[f17]) ).
fof(f225,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,[],[f224]) ).
fof(f226,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,[],[f225]) ).
fof(f227,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(sK11(X0,X1,X2),X2)
| ( ~ in(sK11(X0,X1,X2),X1)
& in(sK11(X0,X1,X2),X0) ) )
& ( ~ in(sK11(X0,X1,X2),X2)
| in(sK11(X0,X1,X2),X1)
| ~ in(sK11(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f226]) ).
fof(f315,plain,
element(sK5,powerset(sK3)),
inference(cnf_transformation,[],[f203]) ).
fof(f316,plain,
in(sK4,sK5),
inference(cnf_transformation,[],[f203]) ).
fof(f317,plain,
in(sK4,subset_complement(sK3,sK5)),
inference(cnf_transformation,[],[f203]) ).
fof(f366,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f424,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
fof(f504,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f366]) ).
tcf(c_111,negated_conjecture,
in(sK4,subset_complement(sK3,sK5)),
inference(cnf_transformation,[],[f317]) ).
tcf(c_112,negated_conjecture,
in(sK4,sK5),
inference(cnf_transformation,[],[f316]) ).
tcf(c_113,negated_conjecture,
element(sK5,powerset(sK3)),
inference(cnf_transformation,[],[f315]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f424]) ).
tcf(c_13349,plain,
set_difference(sK3,sK5) = subset_complement(sK3,sK5),
inference(superposition,[status(thm)],[c_113,c_218]) ).
tcf(c_13391,plain,
in(sK4,set_difference(sK3,sK5)),
inference(demodulation,[status(thm)],[c_111,c_13349]) ).
tcf(c_13850,plain,
~ in(sK4,sK5),
inference(superposition,[status(thm)],[c_13391,c_166]) ).
tcf(c_13853,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13850,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU172+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 13:03:12 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 0.91/1.29 % SZS status Started for theBenchmark.p
% 0.91/1.29 % SZS status Theorem for theBenchmark.p
% 0.91/1.29
% 0.91/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.91/1.29
% 0.91/1.29 % ------ iProver source info
% 0.91/1.29
% 0.91/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.91/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.91/1.29 % git: non_committed_changes: false
% 0.91/1.29
% 0.91/1.29 % ------ Parsing...
% 0.91/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.91/1.29
% 0.91/1.29 % ------ Preprocessing... sup_sim: 6 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 %
% 0.91/1.29
% 0.91/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.91/1.29
% 0.91/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.91/1.29 % ------ Proving...
% 0.91/1.29 % ------ Problem Properties
% 0.91/1.29
% 0.91/1.29 %
% 0.91/1.29 % clauses 154
% 0.91/1.29 % conjectures 3
% 0.91/1.29 % EPR 26
% 0.91/1.29 % Horn 122
% 0.91/1.29 % unary 34
% 0.91/1.29 % binary 65
% 0.91/1.29 % lits 340
% 0.91/1.29 % lits eq 84
% 0.91/1.29 % fd_pure 0
% 0.91/1.29 % fd_pseudo 0
% 0.91/1.29 % fd_cond 4
% 0.91/1.29 % fd_pseudo_cond 35
% 0.91/1.29 % AC symbols 0
% 0.91/1.29
% 0.91/1.29 % ------ Schedule dynamic 5 is on
% 0.91/1.29
% 0.91/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.91/1.29
% 0.91/1.29
% 0.91/1.29 % ------
% 0.91/1.29 % Current options:
% 0.91/1.29 % ------
% 0.91/1.29
% 0.91/1.29
% 0.91/1.29 %
% 0.91/1.29
% 0.91/1.29 % ------ Proving...
% 0.91/1.29 %
% 0.91/1.29
% 0.91/1.29 % SZS status Theorem for theBenchmark.p
% 0.91/1.29
% 0.91/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.91/1.29
% 0.91/1.29
%------------------------------------------------------------------------------