TSTP Solution File: SET975+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 15:10:53 EDT 2023
% Result : Theorem 2.02s 1.15s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 11 unt; 0 def)
% Number of atoms : 177 ( 61 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 201 ( 81 ~; 83 |; 29 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 121 ( 5 sgn; 77 !; 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] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<~> ( in(X1,X3)
& X0 = X2 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f15]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f17]) ).
fof(f23,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f24,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( ? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) )
=> ( ( ~ in(sK4,sK6)
| sK3 != sK5
| ~ in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) )
& ( ( in(sK4,sK6)
& sK3 = sK5 )
| in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ( ~ in(sK4,sK6)
| sK3 != sK5
| ~ in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) )
& ( ( in(sK4,sK6)
& sK3 = sK5 )
| in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f24,f25]) ).
fof(f28,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f29,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
( sK3 = sK5
| in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
( in(sK4,sK6)
| in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
( ~ in(sK4,sK6)
| sK3 != sK5
| ~ in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f37,f33]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f36,f33]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f35,f33]) ).
fof(f47,plain,
( ~ in(sK4,sK6)
| sK3 != sK5
| ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
inference(definition_unfolding,[],[f42,f33]) ).
fof(f48,plain,
( in(sK4,sK6)
| in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
inference(definition_unfolding,[],[f41,f33]) ).
fof(f49,plain,
( sK3 = sK5
| in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
inference(definition_unfolding,[],[f40,f33]) ).
fof(f50,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f30]) ).
fof(f51,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f50]) ).
fof(f52,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f29]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f28]) ).
cnf(c_53,plain,
in(X0,singleton(X0)),
inference(cnf_transformation,[],[f51]) ).
cnf(c_54,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_56,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1)) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_57,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_58,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_61,negated_conjecture,
( sK3 != sK5
| ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6))
| ~ in(sK4,sK6) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_62,negated_conjecture,
( in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6))
| in(sK4,sK6) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_63,negated_conjecture,
( sK3 = sK5
| in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_93,plain,
in(sK4,sK6),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_57]) ).
cnf(c_95,plain,
( sK3 != sK5
| ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_57]) ).
cnf(c_135,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(demodulation,[status(thm)],[c_58,c_50]) ).
cnf(c_145,plain,
( sK3 = sK5
| in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(singleton(sK5),sK6)) ),
inference(demodulation,[status(thm)],[c_63,c_50]) ).
cnf(c_156,plain,
( sK3 != sK5
| ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(singleton(sK5),sK6)) ),
inference(demodulation,[status(thm)],[c_95,c_50]) ).
cnf(c_161,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) ),
inference(demodulation,[status(thm)],[c_56,c_50]) ).
cnf(c_536,plain,
( sK3 = sK5
| in(sK3,singleton(sK5)) ),
inference(superposition,[status(thm)],[c_145,c_135]) ).
cnf(c_561,plain,
sK3 = sK5,
inference(forward_subsumption_resolution,[status(thm)],[c_536,c_54]) ).
cnf(c_562,plain,
( sK3 != sK3
| ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(singleton(sK3),sK6)) ),
inference(demodulation,[status(thm)],[c_156,c_561]) ).
cnf(c_563,plain,
~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(singleton(sK3),sK6)),
inference(equality_resolution_simp,[status(thm)],[c_562]) ).
cnf(c_620,plain,
( ~ in(sK3,singleton(sK3))
| ~ in(sK4,sK6) ),
inference(superposition,[status(thm)],[c_161,c_563]) ).
cnf(c_621,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_620,c_93,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n008.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 : Sat Aug 26 12:23:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.02/1.15 % SZS status Started for theBenchmark.p
% 2.02/1.15 % SZS status Theorem for theBenchmark.p
% 2.02/1.15
% 2.02/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.02/1.15
% 2.02/1.15 ------ iProver source info
% 2.02/1.15
% 2.02/1.15 git: date: 2023-05-31 18:12:56 +0000
% 2.02/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.02/1.15 git: non_committed_changes: false
% 2.02/1.15 git: last_make_outside_of_git: false
% 2.02/1.15
% 2.02/1.15 ------ Parsing...
% 2.02/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.02/1.15
% 2.02/1.15 ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.02/1.15
% 2.02/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.02/1.15
% 2.02/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.02/1.15 ------ Proving...
% 2.02/1.15 ------ Problem Properties
% 2.02/1.15
% 2.02/1.15
% 2.02/1.15 clauses 15
% 2.02/1.15 conjectures 0
% 2.02/1.15 EPR 4
% 2.02/1.15 Horn 13
% 2.02/1.15 unary 6
% 2.02/1.15 binary 6
% 2.02/1.15 lits 27
% 2.02/1.15 lits eq 8
% 2.02/1.15 fd_pure 0
% 2.02/1.15 fd_pseudo 0
% 2.02/1.15 fd_cond 0
% 2.02/1.15 fd_pseudo_cond 2
% 2.02/1.15 AC symbols 0
% 2.02/1.15
% 2.02/1.15 ------ Schedule dynamic 5 is on
% 2.02/1.15
% 2.02/1.15 ------ no conjectures: strip conj schedule
% 2.02/1.15
% 2.02/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.02/1.15
% 2.02/1.15
% 2.02/1.15 ------
% 2.02/1.15 Current options:
% 2.02/1.15 ------
% 2.02/1.15
% 2.02/1.15
% 2.02/1.15
% 2.02/1.15
% 2.02/1.15 ------ Proving...
% 2.02/1.15
% 2.02/1.15
% 2.02/1.15 % SZS status Theorem for theBenchmark.p
% 2.02/1.15
% 2.02/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.02/1.15
% 2.02/1.15
%------------------------------------------------------------------------------