%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU124+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 : n018.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 02:55:29 PM UTC 2026
% Result : Theorem 2.31s 1.27s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 10 unt; 1 def)
% Number of atoms : 118 ( 11 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 135 ( 51 ~; 53 |; 26 &)
% ( 4 <=>; 1 =>; 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn 59 !; 7 ?; 9 :)
% 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(f17,conjecture,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f28,plain,
? [X0,X1] : ~ subset(X0,set_union2(X0,X1)),
inference(ennf_transformation,[],[f18]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f32,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,[],[f31]) ).
fof(f33,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))],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f35]) ).
fof(f39,plain,
~ subset(sK4,set_union2(sK4,sK5)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f28]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
~ subset(sK4,set_union2(sK4,sK5)),
inference(cnf_transformation,[],[f39]) ).
fof(f63,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f44]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_70,negated_conjecture,
~ subset(sK4,set_union2(sK4,sK5)),
inference(cnf_transformation,[],[f61]) ).
tcf(c_296,definition,
iPr_def_10 = set_union2(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_297,negated_conjecture,
~ subset(sK4,iPr_def_10),
inference(demodulation,[status(thm)],[c_70,c_296]) ).
tcf(c_642,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_296,c_54]) ).
tcf(c_659,plain,
! [X0: $i] :
( subset(sK4,X0)
| in(sK1(sK4,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_58,c_642]) ).
tcf(c_756,plain,
subset(sK4,iPr_def_10),
inference(superposition,[status(thm)],[c_659,c_57]) ).
tcf(c_757,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_756,c_297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU124+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n018.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:51:18 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
% 0.12/0.43 % Proving...
% 2.31/1.27 % SZS status Started for theBenchmark.p
% 2.31/1.27 % SZS status Theorem for theBenchmark.p
% 2.31/1.27
% 2.31/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.31/1.27
% 2.31/1.27 % ------ iProver source info
% 2.31/1.27
% 2.31/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.31/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.31/1.27 % git: non_committed_changes: false
% 2.31/1.27
% 2.31/1.27 % ------ Parsing...
% 2.31/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.31/1.27
% 2.31/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.31/1.27
% 2.31/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.31/1.27
% 2.31/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.31/1.27 % ------ Proving...
% 2.31/1.27 % ------ Problem Properties
% 2.31/1.27
% 2.31/1.27 %
% 2.31/1.27 % clauses 24
% 2.31/1.27 % conjectures 1
% 2.31/1.27 % EPR 10
% 2.31/1.27 % Horn 21
% 2.31/1.27 % unary 9
% 2.31/1.27 % binary 9
% 2.31/1.27 % lits 46
% 2.31/1.27 % lits eq 9
% 2.31/1.27 % fd_pure 0
% 2.31/1.27 % fd_pseudo 0
% 2.31/1.27 % fd_cond 1
% 2.31/1.27 % fd_pseudo_cond 4
% 2.31/1.27 % AC symbols 0
% 2.31/1.27
% 2.31/1.27 % ------ Schedule dynamic 5 is on
% 2.31/1.27
% 2.31/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.31/1.27
% 2.31/1.27
% 2.31/1.27 % ------
% 2.31/1.27 % Current options:
% 2.31/1.27 % ------
% 2.31/1.27
% 2.31/1.27
% 2.31/1.27 %
% 2.31/1.27
% 2.31/1.27 % ------ Proving...
% 2.31/1.27 %
% 2.31/1.27
% 2.31/1.27 % SZS status Theorem for theBenchmark.p
% 2.31/1.27
% 2.31/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.31/1.27
% 2.31/1.27
%------------------------------------------------------------------------------