%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU129+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 : n014.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 02:55:30 PM UTC 2026
% Result : Theorem 2.85s 1.29s
% Output : CNFRefutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 14 unt; 2 def)
% Number of atoms : 193 ( 17 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 189 ( 74 ~; 79 |; 29 &)
% ( 4 <=>; 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 109 ( 0 sgn 101 !; 8 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f22,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f26,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,[],[f21]) ).
fof(f27,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,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f27]) ).
fof(f29,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,[],[f4]) ).
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(flattening,[],[f29]) ).
fof(f31,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,[],[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) ) ) )
& ( ( ( 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_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f31]) ).
fof(f35,plain,
( subset(sK4,sK5)
& ~ subset(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f22]) ).
fof(f37,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f39,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f40,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f42,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
~ subset(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),
inference(cnf_transformation,[],[f35]) ).
fof(f58,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f43]) ).
fof(f59,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f42]) ).
fof(f60,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f41]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_65,negated_conjecture,
~ subset(set_intersection2(sK4,sK6),set_intersection2(sK5,sK6)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_66,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f52]) ).
tcf(c_172,plain,
~ subset(set_intersection2(sK4,sK6),set_intersection2(sK6,sK5)),
inference(demodulation,[status(thm)],[c_65,c_50]) ).
tcf(c_302,definition,
iPr_def_10 = set_intersection2(sK4,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_303,definition,
iPr_def_11 = set_intersection2(sK6,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_304,plain,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_172,c_303,c_302]) ).
tcf(c_305,negated_conjecture,
subset(sK4,sK5),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_614,plain,
! [X0: $i] :
( in(X0,sK4)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_302,c_58]) ).
tcf(c_633,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),sK4) ),
inference(superposition,[status(thm)],[c_52,c_614]) ).
tcf(c_673,plain,
! [X0: $i] :
( in(X0,sK6)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_302,c_59]) ).
tcf(c_699,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_10,X1)
| in(sK0(iPr_def_10,X1),X0)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_633,c_53]) ).
tcf(c_719,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,sK5)
| ~ in(X0,sK6) ),
inference(superposition,[status(thm)],[c_303,c_57]) ).
tcf(c_757,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),sK6) ),
inference(superposition,[status(thm)],[c_52,c_673]) ).
tcf(c_1729,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),iPr_def_11)
| ~ subset(sK4,sK5)
| ~ in(sK0(iPr_def_10,X0),sK6) ),
inference(superposition,[status(thm)],[c_699,c_719]) ).
tcf(c_1763,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),iPr_def_11)
| ~ in(sK0(iPr_def_10,X0),sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1729,c_305]) ).
tcf(c_1780,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_1763,c_757,c_1763]) ).
tcf(c_1790,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1780,c_51]) ).
tcf(c_1793,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1790,c_304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:51:35 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.85/1.29 % SZS status Started for theBenchmark.p
% 2.85/1.29 % SZS status Theorem for theBenchmark.p
% 2.85/1.29
% 2.85/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.85/1.29
% 2.85/1.29 % ------ iProver source info
% 2.85/1.29
% 2.85/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.85/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.85/1.29 % git: non_committed_changes: false
% 2.85/1.29
% 2.85/1.29 % ------ Parsing...
% 2.85/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.85/1.29
% 2.85/1.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.85/1.29
% 2.85/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.85/1.29
% 2.85/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.85/1.29 % ------ Proving...
% 2.85/1.29 % ------ Problem Properties
% 2.85/1.29
% 2.85/1.29 %
% 2.85/1.29 % clauses 24
% 2.85/1.29 % conjectures 1
% 2.85/1.29 % EPR 11
% 2.85/1.29 % Horn 21
% 2.85/1.29 % unary 11
% 2.85/1.29 % binary 7
% 2.85/1.29 % lits 44
% 2.85/1.29 % lits eq 10
% 2.85/1.29 % fd_pure 0
% 2.85/1.29 % fd_pseudo 0
% 2.85/1.29 % fd_cond 1
% 2.85/1.29 % fd_pseudo_cond 4
% 2.85/1.29 % AC symbols 0
% 2.85/1.29
% 2.85/1.29 % ------ Schedule dynamic 5 is on
% 2.85/1.29
% 2.85/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.85/1.29
% 2.85/1.29
% 2.85/1.29 % ------
% 2.85/1.29 % Current options:
% 2.85/1.29 % ------
% 2.85/1.29
% 2.85/1.29
% 2.85/1.29 %
% 2.85/1.29
% 2.85/1.29 % ------ Proving...
% 2.85/1.29 %
% 2.85/1.29
% 2.85/1.29 % SZS status Theorem for theBenchmark.p
% 2.85/1.29
% 2.85/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.85/1.29
% 2.85/1.29
%------------------------------------------------------------------------------