TSTP Solution File: SEU159+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU159+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:04:13 EDT 2023
% Result : Theorem 2.53s 1.15s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 12 unt; 0 def)
% Number of atoms : 222 ( 73 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 256 ( 94 ~; 106 |; 45 &)
% ( 6 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 126 ( 4 sgn; 82 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
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(f8,conjecture,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
inference(negated_conjecture,[],[f8]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f13,plain,
? [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<~> ( in(X1,X2)
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,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
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = 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
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f21]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ( ~ in(X1,X2)
| ~ in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ~ in(X1,X2)
| ~ in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
( ? [X0,X1,X2] :
( ( ~ in(X1,X2)
| ~ in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| subset(unordered_pair(X0,X1),X2) ) )
=> ( ( ~ in(sK5,sK6)
| ~ in(sK4,sK6)
| ~ subset(unordered_pair(sK4,sK5),sK6) )
& ( ( in(sK5,sK6)
& in(sK4,sK6) )
| subset(unordered_pair(sK4,sK5),sK6) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
( ( ~ in(sK5,sK6)
| ~ in(sK4,sK6)
| ~ subset(unordered_pair(sK4,sK5),sK6) )
& ( ( in(sK5,sK6)
& in(sK4,sK6) )
| subset(unordered_pair(sK4,sK5),sK6) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f28,f29]) ).
fof(f32,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
( in(sK4,sK6)
| subset(unordered_pair(sK4,sK5),sK6) ),
inference(cnf_transformation,[],[f30]) ).
fof(f46,plain,
( in(sK5,sK6)
| subset(unordered_pair(sK4,sK5),sK6) ),
inference(cnf_transformation,[],[f30]) ).
fof(f47,plain,
( ~ in(sK5,sK6)
| ~ in(sK4,sK6)
| ~ subset(unordered_pair(sK4,sK5),sK6) ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f35]) ).
fof(f49,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f48]) ).
fof(f50,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f34]) ).
fof(f51,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_resolution,[],[f33]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f32]) ).
cnf(c_54,plain,
in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f49]) ).
cnf(c_55,plain,
in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
cnf(c_56,plain,
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_57,plain,
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_58,plain,
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_59,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_63,negated_conjecture,
( ~ subset(unordered_pair(sK4,sK5),sK6)
| ~ in(sK5,sK6)
| ~ in(sK4,sK6) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_64,negated_conjecture,
( subset(unordered_pair(sK4,sK5),sK6)
| in(sK5,sK6) ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_65,negated_conjecture,
( subset(unordered_pair(sK4,sK5),sK6)
| in(sK4,sK6) ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_153,plain,
( subset(unordered_pair(sK5,sK4),sK6)
| in(sK5,sK6) ),
inference(demodulation,[status(thm)],[c_64,c_50]) ).
cnf(c_154,plain,
( subset(unordered_pair(sK5,sK4),sK6)
| in(sK4,sK6) ),
inference(demodulation,[status(thm)],[c_65,c_50]) ).
cnf(c_177,plain,
( ~ subset(unordered_pair(sK5,sK4),sK6)
| ~ in(sK5,sK6)
| ~ in(sK4,sK6) ),
inference(demodulation,[status(thm)],[c_63,c_50]) ).
cnf(c_809,plain,
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(superposition,[status(thm)],[c_54,c_59]) ).
cnf(c_810,plain,
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(superposition,[status(thm)],[c_55,c_59]) ).
cnf(c_830,plain,
in(sK4,sK6),
inference(backward_subsumption_resolution,[status(thm)],[c_154,c_809]) ).
cnf(c_831,plain,
( ~ subset(unordered_pair(sK5,sK4),sK6)
| ~ in(sK5,sK6) ),
inference(backward_subsumption_resolution,[status(thm)],[c_177,c_809]) ).
cnf(c_856,plain,
in(sK5,sK6),
inference(backward_subsumption_resolution,[status(thm)],[c_153,c_810]) ).
cnf(c_857,plain,
~ subset(unordered_pair(sK5,sK4),sK6),
inference(backward_subsumption_resolution,[status(thm)],[c_831,c_810]) ).
cnf(c_898,plain,
( sK1(unordered_pair(X0,X1),X2) = X0
| sK1(unordered_pair(X0,X1),X2) = X1
| subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_56]) ).
cnf(c_1003,plain,
( sK1(unordered_pair(sK5,sK4),sK6) = sK5
| sK1(unordered_pair(sK5,sK4),sK6) = sK4 ),
inference(superposition,[status(thm)],[c_898,c_857]) ).
cnf(c_1042,plain,
( ~ in(sK4,sK6)
| sK1(unordered_pair(sK5,sK4),sK6) = sK5
| subset(unordered_pair(sK5,sK4),sK6) ),
inference(superposition,[status(thm)],[c_1003,c_57]) ).
cnf(c_1047,plain,
sK1(unordered_pair(sK5,sK4),sK6) = sK5,
inference(forward_subsumption_resolution,[status(thm)],[c_1042,c_857,c_830]) ).
cnf(c_1051,plain,
( ~ in(sK5,sK6)
| subset(unordered_pair(sK5,sK4),sK6) ),
inference(superposition,[status(thm)],[c_1047,c_57]) ).
cnf(c_1056,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1051,c_857,c_856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU159+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 13:28:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.53/1.15 % SZS status Started for theBenchmark.p
% 2.53/1.15 % SZS status Theorem for theBenchmark.p
% 2.53/1.15
% 2.53/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.53/1.15
% 2.53/1.15 ------ iProver source info
% 2.53/1.15
% 2.53/1.15 git: date: 2023-05-31 18:12:56 +0000
% 2.53/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.53/1.15 git: non_committed_changes: false
% 2.53/1.15 git: last_make_outside_of_git: false
% 2.53/1.15
% 2.53/1.15 ------ Parsing...
% 2.53/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.53/1.15
% 2.53/1.15 ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 2.53/1.15
% 2.53/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.53/1.15
% 2.53/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.53/1.15 ------ Proving...
% 2.53/1.15 ------ Problem Properties
% 2.53/1.15
% 2.53/1.15
% 2.53/1.15 clauses 16
% 2.53/1.15 conjectures 0
% 2.53/1.15 EPR 4
% 2.53/1.15 Horn 11
% 2.53/1.15 unary 5
% 2.53/1.15 binary 5
% 2.53/1.15 lits 34
% 2.53/1.15 lits eq 11
% 2.53/1.15 fd_pure 0
% 2.53/1.15 fd_pseudo 0
% 2.53/1.15 fd_cond 0
% 2.53/1.15 fd_pseudo_cond 3
% 2.53/1.15 AC symbols 0
% 2.53/1.15
% 2.53/1.15 ------ Schedule dynamic 5 is on
% 2.53/1.15
% 2.53/1.15 ------ no conjectures: strip conj schedule
% 2.53/1.15
% 2.53/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.53/1.15
% 2.53/1.15
% 2.53/1.15 ------
% 2.53/1.15 Current options:
% 2.53/1.15 ------
% 2.53/1.15
% 2.53/1.15
% 2.53/1.15
% 2.53/1.15
% 2.53/1.15 ------ Proving...
% 2.53/1.15
% 2.53/1.15
% 2.53/1.15 % SZS status Theorem for theBenchmark.p
% 2.53/1.15
% 2.53/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.53/1.15
% 2.53/1.15
%------------------------------------------------------------------------------