%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU159+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 : n006.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 02:55:39 PM UTC 2026
% Result : Theorem 2.58s 1.16s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 59 ( 12 unt; 1 def)
% Number of atoms : 220 ( 65 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 222 ( 82 ~; 97 |; 35 &)
% ( 6 <=>; 1 =>; 0 <=; 1 <~>)
% 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 0 sgn 91 !; 14 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f12,plain,
? [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<~> ( in(X1,X2)
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X0 )
& ( ~ in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f15]) ).
fof(f17,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,[],[f11]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
( ( subset(unordered_pair(sK2,sK3),sK4)
| ( in(sK3,sK4)
& in(sK2,sK4) ) )
& ( ~ subset(unordered_pair(sK2,sK3),sK4)
| ~ in(sK3,sK4)
| ~ in(sK2,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f21]) ).
fof(f25,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
( subset(unordered_pair(sK2,sK3),sK4)
| in(sK3,sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
( subset(unordered_pair(sK2,sK3),sK4)
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
( ~ subset(unordered_pair(sK2,sK3),sK4)
| ~ in(sK3,sK4)
| ~ in(sK2,sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f27]) ).
fof(f39,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f38]) ).
fof(f40,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f26]) ).
fof(f41,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_61,negated_conjecture,
( ~ in(sK3,sK4)
| ~ in(sK2,sK4)
| ~ subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,negated_conjecture,
( in(sK2,sK4)
| subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_63,negated_conjecture,
( in(sK3,sK4)
| subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_303,definition,
iPr_def_10 = unordered_pair(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_304,negated_conjecture,
( subset(iPr_def_10,sK4)
| in(sK3,sK4) ),
inference(demodulation,[status(thm)],[c_63,c_303]) ).
tcf(c_305,negated_conjecture,
( subset(iPr_def_10,sK4)
| in(sK2,sK4) ),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_306,negated_conjecture,
( ~ subset(iPr_def_10,sK4)
| ~ in(sK3,sK4)
| ~ in(sK2,sK4) ),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_525,plain,
in(sK3,iPr_def_10),
inference(superposition,[status(thm)],[c_303,c_55]) ).
tcf(c_526,plain,
in(sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_303,c_54]) ).
tcf(c_571,plain,
! [X0: $i] :
( in(sK3,X0)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_525,c_59]) ).
tcf(c_572,plain,
! [X0: $i] :
( in(sK2,X0)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_526,c_59]) ).
tcf(c_584,plain,
( in(sK2,sK4)
| ~ subset(iPr_def_10,sK4) ),
inference(instantiation,[status(thm)],[c_572]) ).
tcf(c_591,plain,
in(sK3,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_304,c_571]) ).
tcf(c_592,plain,
( ~ subset(iPr_def_10,sK4)
| ~ in(sK2,sK4) ),
inference(backward_subsumption_resolution,[status(thm)],[c_306,c_571]) ).
tcf(c_601,plain,
~ subset(iPr_def_10,sK4),
inference(global_subsumption_just,[status(thm)],[c_592,c_584,c_592]) ).
tcf(c_603,plain,
in(sK2,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_305,c_601]) ).
tcf(c_627,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ( X0 = sK2 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_303,c_56]) ).
tcf(c_733,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ( sK1(iPr_def_10,X0) = sK3 )
| ( sK1(iPr_def_10,X0) = sK2 ) ),
inference(superposition,[status(thm)],[c_58,c_627]) ).
tcf(c_781,plain,
( ( sK1(iPr_def_10,sK4) = sK3 )
| ( sK1(iPr_def_10,sK4) = sK2 ) ),
inference(superposition,[status(thm)],[c_733,c_601]) ).
tcf(c_797,plain,
( subset(iPr_def_10,sK4)
| ( sK1(iPr_def_10,sK4) = sK2 )
| ~ in(sK3,sK4) ),
inference(superposition,[status(thm)],[c_781,c_57]) ).
tcf(c_801,plain,
sK1(iPr_def_10,sK4) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_797,c_601,c_591]) ).
tcf(c_803,plain,
( subset(iPr_def_10,sK4)
| ~ in(sK2,sK4) ),
inference(superposition,[status(thm)],[c_801,c_57]) ).
tcf(c_807,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_803,c_601,c_603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU159+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n006.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 12:59:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.58/1.16 % SZS status Started for theBenchmark.p
% 2.58/1.16 % SZS status Theorem for theBenchmark.p
% 2.58/1.16
% 2.58/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.58/1.16
% 2.58/1.16 % ------ iProver source info
% 2.58/1.16
% 2.58/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 2.58/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.58/1.16 % git: non_committed_changes: false
% 2.58/1.16
% 2.58/1.16 % ------ Parsing...
% 2.58/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.58/1.16
% 2.58/1.16 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.58/1.16
% 2.58/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.58/1.16
% 2.58/1.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.58/1.16 % ------ Proving...
% 2.58/1.16 % ------ Problem Properties
% 2.58/1.16
% 2.58/1.16 %
% 2.58/1.16 % clauses 16
% 2.58/1.16 % conjectures 3
% 2.58/1.16 % EPR 6
% 2.58/1.16 % Horn 11
% 2.58/1.16 % unary 5
% 2.58/1.16 % binary 5
% 2.58/1.16 % lits 34
% 2.58/1.16 % lits eq 11
% 2.58/1.16 % fd_pure 0
% 2.58/1.16 % fd_pseudo 0
% 2.58/1.16 % fd_cond 0
% 2.58/1.16 % fd_pseudo_cond 3
% 2.58/1.16 % AC symbols 0
% 2.58/1.16
% 2.58/1.16 % ------ Schedule dynamic 5 is on
% 2.58/1.16
% 2.58/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.58/1.16
% 2.58/1.16
% 2.58/1.16 % ------
% 2.58/1.16 % Current options:
% 2.58/1.16 % ------
% 2.58/1.16
% 2.58/1.16
% 2.58/1.16 %
% 2.58/1.16
% 2.58/1.16 % ------ Proving...
% 2.58/1.16 %
% 2.58/1.16
% 2.58/1.16 % SZS status Theorem for theBenchmark.p
% 2.58/1.16
% 2.58/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.58/1.16
% 2.58/1.16
%------------------------------------------------------------------------------