%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU124+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 : 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 02:55:29 PM UTC 2026
% Result : Theorem 3.05s 1.27s
% Output : CNFRefutation 3.05s
% 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(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(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f30,conjecture,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f50,plain,
? [X0,X1] : ~ subset(X0,set_union2(X0,X1)),
inference(ennf_transformation,[],[f31]) ).
fof(f57,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(f58,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,[],[f57]) ).
fof(f59,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,[],[f58]) ).
fof(f60,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))],[f59]) ).
fof(f61,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,[],[f39]) ).
fof(f62,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,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK2(X0,X1),X0)
& ~ in(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f62]) ).
fof(f73,plain,
~ subset(sK8,set_union2(sK8,sK9)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f50]) ).
fof(f84,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f89,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f90,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f119,plain,
~ subset(sK8,set_union2(sK8,sK9)),
inference(cnf_transformation,[],[f73]) ).
fof(f124,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f84]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_94,negated_conjecture,
~ subset(sK8,set_union2(sK8,sK9)),
inference(cnf_transformation,[],[f119]) ).
tcf(c_1099,definition,
iPr_def_10 = set_union2(sK8,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1100,negated_conjecture,
~ subset(sK8,iPr_def_10),
inference(demodulation,[status(thm)],[c_94,c_1099]) ).
tcf(c_1983,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,sK8) ),
inference(superposition,[status(thm)],[c_1099,c_60]) ).
tcf(c_2023,plain,
! [X0: $i] :
( subset(sK8,X0)
| in(sK2(sK8,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_64,c_1983]) ).
tcf(c_2116,plain,
subset(sK8,iPr_def_10),
inference(superposition,[status(thm)],[c_2023,c_63]) ).
tcf(c_2117,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2116,c_1100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 12:49:27 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...
% 3.05/1.27 % SZS status Started for theBenchmark.p
% 3.05/1.27 % SZS status Theorem for theBenchmark.p
% 3.05/1.27
% 3.05/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.05/1.27
% 3.05/1.27 % ------ iProver source info
% 3.05/1.27
% 3.05/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.05/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.05/1.27 % git: non_committed_changes: false
% 3.05/1.27
% 3.05/1.27 % ------ Parsing...
% 3.05/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.05/1.27
% 3.05/1.27 % ------ 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 %
% 3.05/1.27
% 3.05/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.05/1.27
% 3.05/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.05/1.27 % ------ Proving...
% 3.05/1.27 % ------ Problem Properties
% 3.05/1.27
% 3.05/1.27 %
% 3.05/1.27 % clauses 46
% 3.05/1.27 % conjectures 1
% 3.05/1.27 % EPR 17
% 3.05/1.27 % Horn 37
% 3.05/1.27 % unary 13
% 3.05/1.27 % binary 20
% 3.05/1.27 % lits 94
% 3.05/1.28 % lits eq 19
% 3.05/1.28 % fd_pure 0
% 3.05/1.28 % fd_pseudo 0
% 3.05/1.28 % fd_cond 3
% 3.05/1.28 % fd_pseudo_cond 8
% 3.05/1.28 % AC symbols 0
% 3.05/1.28
% 3.05/1.28 % ------ Schedule dynamic 5 is on
% 3.05/1.28
% 3.05/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.05/1.28
% 3.05/1.28
% 3.05/1.28 % ------
% 3.05/1.28 % Current options:
% 3.05/1.28 % ------
% 3.05/1.28
% 3.05/1.28
% 3.05/1.28 %
% 3.05/1.28
% 3.05/1.28 % ------ Proving...
% 3.05/1.28 %
% 3.05/1.28
% 3.05/1.28 % SZS status Theorem for theBenchmark.p
% 3.05/1.28
% 3.05/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.05/1.28
% 3.05/1.28
%------------------------------------------------------------------------------