TSTP Solution File: SET954+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 15:10:48 EDT 2023
% Result : Theorem 2.31s 1.17s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 17 unt; 0 def)
% Number of atoms : 78 ( 5 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 74 ( 36 ~; 25 |; 9 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 9 sgn; 52 !; 8 ?)
% 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] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f5,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(f8,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
=> in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
=> in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
inference(negated_conjecture,[],[f8]) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
& in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,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,[],[f5]) ).
fof(f13,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,[],[f12]) ).
fof(f18,plain,
( ? [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
& in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
=> ( ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4))
& in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
( ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4))
& in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f11,f18]) ).
fof(f21,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4)),
inference(cnf_transformation,[],[f19]) ).
fof(f32,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,[],[f26,f22]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f25,f22]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f24,f22]) ).
fof(f35,plain,
~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),cartesian_product2(sK5,sK4)),
inference(definition_unfolding,[],[f30,f22]) ).
fof(f36,plain,
in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)),
inference(definition_unfolding,[],[f29,f22]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f21]) ).
cnf(c_52,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1)) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_53,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_54,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_57,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),cartesian_product2(sK5,sK4)),
inference(cnf_transformation,[],[f35]) ).
cnf(c_58,negated_conjecture,
in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f36]) ).
cnf(c_96,plain,
in(unordered_pair(singleton(sK2),unordered_pair(sK3,sK2)),cartesian_product2(sK4,sK5)),
inference(demodulation,[status(thm)],[c_58,c_50]) ).
cnf(c_97,plain,
~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),cartesian_product2(sK5,sK4)),
inference(demodulation,[status(thm)],[c_57,c_50]) ).
cnf(c_98,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(demodulation,[status(thm)],[c_54,c_50]) ).
cnf(c_103,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(demodulation,[status(thm)],[c_53,c_50]) ).
cnf(c_108,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_52,c_50]) ).
cnf(c_295,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(superposition,[status(thm)],[c_50,c_98]) ).
cnf(c_303,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(superposition,[status(thm)],[c_50,c_103]) ).
cnf(c_316,plain,
( ~ in(sK3,sK5)
| ~ in(sK2,sK4) ),
inference(superposition,[status(thm)],[c_108,c_97]) ).
cnf(c_337,plain,
in(sK2,sK4),
inference(superposition,[status(thm)],[c_96,c_295]) ).
cnf(c_341,plain,
~ in(sK3,sK5),
inference(backward_subsumption_resolution,[status(thm)],[c_316,c_337]) ).
cnf(c_347,plain,
in(sK3,sK5),
inference(superposition,[status(thm)],[c_96,c_303]) ).
cnf(c_351,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_347,c_341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.36 % Computer : n014.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 08:29:32 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.31/1.17 % SZS status Started for theBenchmark.p
% 2.31/1.17 % SZS status Theorem for theBenchmark.p
% 2.31/1.17
% 2.31/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.31/1.17
% 2.31/1.17 ------ iProver source info
% 2.31/1.17
% 2.31/1.17 git: date: 2023-05-31 18:12:56 +0000
% 2.31/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.31/1.17 git: non_committed_changes: false
% 2.31/1.17 git: last_make_outside_of_git: false
% 2.31/1.17
% 2.31/1.17 ------ Parsing...
% 2.31/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.31/1.17
% 2.31/1.17 ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.31/1.17
% 2.31/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.31/1.17
% 2.31/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.31/1.17 ------ Proving...
% 2.31/1.17 ------ Problem Properties
% 2.31/1.17
% 2.31/1.17
% 2.31/1.17 clauses 10
% 2.31/1.17 conjectures 0
% 2.31/1.17 EPR 3
% 2.31/1.17 Horn 10
% 2.31/1.17 unary 6
% 2.31/1.17 binary 3
% 2.31/1.17 lits 15
% 2.31/1.17 lits eq 1
% 2.31/1.17 fd_pure 0
% 2.31/1.17 fd_pseudo 0
% 2.31/1.17 fd_cond 0
% 2.31/1.17 fd_pseudo_cond 0
% 2.31/1.17 AC symbols 0
% 2.31/1.17
% 2.31/1.17 ------ Schedule dynamic 5 is on
% 2.31/1.17
% 2.31/1.17 ------ no conjectures: strip conj schedule
% 2.31/1.17
% 2.31/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.31/1.17
% 2.31/1.17
% 2.31/1.17 ------
% 2.31/1.17 Current options:
% 2.31/1.17 ------
% 2.31/1.17
% 2.31/1.17
% 2.31/1.17
% 2.31/1.17
% 2.31/1.17 ------ Proving...
% 2.31/1.17
% 2.31/1.17
% 2.31/1.17 % SZS status Theorem for theBenchmark.p
% 2.31/1.17
% 2.31/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.31/1.17
% 2.31/1.17
%------------------------------------------------------------------------------