TSTP Solution File: SEU159+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 2.63s 1.16s
% Output : CNFRefutation 2.63s
% 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(f7,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(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
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] :
( ( ( 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(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(flattening,[],[f13]) ).
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) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f14]) ).
fof(f16,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(f17,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])],[f15,f16]) ).
fof(f18,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,[],[f11]) ).
fof(f19,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,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f21,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])],[f19,f20]) ).
fof(f22,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,[],[f12]) ).
fof(f23,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,[],[f22]) ).
fof(f24,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(sK3,sK4)
| ~ in(sK2,sK4)
| ~ subset(unordered_pair(sK2,sK3),sK4) )
& ( ( in(sK3,sK4)
& in(sK2,sK4) )
| subset(unordered_pair(sK2,sK3),sK4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
( ( ~ in(sK3,sK4)
| ~ in(sK2,sK4)
| ~ subset(unordered_pair(sK2,sK3),sK4) )
& ( ( in(sK3,sK4)
& in(sK2,sK4) )
| subset(unordered_pair(sK2,sK3),sK4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f23,f24]) ).
fof(f27,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
( in(sK2,sK4)
| subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
( in(sK3,sK4)
| subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
( ~ in(sK3,sK4)
| ~ in(sK2,sK4)
| ~ subset(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f30]) ).
fof(f42,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f41]) ).
fof(f43,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f29]) ).
fof(f44,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_resolution,[],[f28]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f27]) ).
cnf(c_54,plain,
in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f42]) ).
cnf(c_55,plain,
in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f44]) ).
cnf(c_56,plain,
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_57,plain,
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_58,plain,
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_59,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_61,negated_conjecture,
( ~ subset(unordered_pair(sK2,sK3),sK4)
| ~ in(sK3,sK4)
| ~ in(sK2,sK4) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_62,negated_conjecture,
( subset(unordered_pair(sK2,sK3),sK4)
| in(sK3,sK4) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_63,negated_conjecture,
( subset(unordered_pair(sK2,sK3),sK4)
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_147,plain,
( subset(unordered_pair(sK3,sK2),sK4)
| in(sK3,sK4) ),
inference(demodulation,[status(thm)],[c_62,c_50]) ).
cnf(c_148,plain,
( subset(unordered_pair(sK3,sK2),sK4)
| in(sK2,sK4) ),
inference(demodulation,[status(thm)],[c_63,c_50]) ).
cnf(c_171,plain,
( ~ subset(unordered_pair(sK3,sK2),sK4)
| ~ in(sK3,sK4)
| ~ in(sK2,sK4) ),
inference(demodulation,[status(thm)],[c_61,c_50]) ).
cnf(c_563,plain,
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(superposition,[status(thm)],[c_54,c_59]) ).
cnf(c_564,plain,
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(superposition,[status(thm)],[c_55,c_59]) ).
cnf(c_582,plain,
in(sK2,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_148,c_563]) ).
cnf(c_583,plain,
( ~ subset(unordered_pair(sK3,sK2),sK4)
| ~ in(sK3,sK4) ),
inference(backward_subsumption_resolution,[status(thm)],[c_171,c_563]) ).
cnf(c_608,plain,
in(sK3,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_147,c_564]) ).
cnf(c_609,plain,
~ subset(unordered_pair(sK3,sK2),sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_583,c_564]) ).
cnf(c_659,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_755,plain,
( sK1(unordered_pair(sK3,sK2),sK4) = sK3
| sK1(unordered_pair(sK3,sK2),sK4) = sK2 ),
inference(superposition,[status(thm)],[c_659,c_609]) ).
cnf(c_795,plain,
( ~ in(sK2,sK4)
| sK1(unordered_pair(sK3,sK2),sK4) = sK3
| subset(unordered_pair(sK3,sK2),sK4) ),
inference(superposition,[status(thm)],[c_755,c_57]) ).
cnf(c_800,plain,
sK1(unordered_pair(sK3,sK2),sK4) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_795,c_609,c_582]) ).
cnf(c_803,plain,
( ~ in(sK3,sK4)
| subset(unordered_pair(sK3,sK2),sK4) ),
inference(superposition,[status(thm)],[c_800,c_57]) ).
cnf(c_808,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_803,c_609,c_608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.19/0.36 % Computer : n007.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Wed Aug 23 12:53:54 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.63/1.16 % SZS status Started for theBenchmark.p
% 2.63/1.16 % SZS status Theorem for theBenchmark.p
% 2.63/1.16
% 2.63/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.63/1.16
% 2.63/1.16 ------ iProver source info
% 2.63/1.16
% 2.63/1.16 git: date: 2023-05-31 18:12:56 +0000
% 2.63/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.63/1.16 git: non_committed_changes: false
% 2.63/1.16 git: last_make_outside_of_git: false
% 2.63/1.16
% 2.63/1.16 ------ Parsing...
% 2.63/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.63/1.16
% 2.63/1.16 ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.63/1.16
% 2.63/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.63/1.16
% 2.63/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.63/1.16 ------ Proving...
% 2.63/1.16 ------ Problem Properties
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16 clauses 15
% 2.63/1.16 conjectures 0
% 2.63/1.16 EPR 3
% 2.63/1.16 Horn 10
% 2.63/1.16 unary 4
% 2.63/1.16 binary 5
% 2.63/1.16 lits 33
% 2.63/1.16 lits eq 10
% 2.63/1.16 fd_pure 0
% 2.63/1.16 fd_pseudo 0
% 2.63/1.16 fd_cond 0
% 2.63/1.16 fd_pseudo_cond 3
% 2.63/1.16 AC symbols 0
% 2.63/1.16
% 2.63/1.16 ------ Schedule dynamic 5 is on
% 2.63/1.16
% 2.63/1.16 ------ no conjectures: strip conj schedule
% 2.63/1.16
% 2.63/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16 ------
% 2.63/1.16 Current options:
% 2.63/1.16 ------
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16 ------ Proving...
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16 % SZS status Theorem for theBenchmark.p
% 2.63/1.16
% 2.63/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.63/1.16
% 2.63/1.16
%------------------------------------------------------------------------------