TSTP Solution File: SET971+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n016.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 15:10:52 EDT 2023
% Result : Theorem 1.87s 1.15s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 53 ( 30 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 40 ( 17 ~; 7 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn; 26 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> cartesian_product2(X0,X2) = set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> cartesian_product2(X0,X2) = set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
& subset(X2,X3)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
& subset(X2,X3)
& subset(X0,X1) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f19,plain,
( ? [X0,X1,X2,X3] :
( cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
& subset(X2,X3)
& subset(X0,X1) )
=> ( cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4))
& subset(sK4,sK5)
& subset(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
( cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4))
& subset(sK4,sK5)
& subset(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f13,f19]) ).
fof(f21,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f6]) ).
fof(f27,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4)),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
cnf(c_49,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f21]) ).
cnf(c_54,plain,
set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
inference(cnf_transformation,[],[f26]) ).
cnf(c_55,negated_conjecture,
set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4)) != cartesian_product2(sK2,sK4),
inference(cnf_transformation,[],[f29]) ).
cnf(c_56,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f28]) ).
cnf(c_57,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f27]) ).
cnf(c_58,plain,
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_101,plain,
( X0 != sK4
| X1 != sK5
| set_intersection2(X0,X1) = X0 ),
inference(resolution_lifted,[status(thm)],[c_56,c_58]) ).
cnf(c_102,plain,
set_intersection2(sK4,sK5) = sK4,
inference(unflattening,[status(thm)],[c_101]) ).
cnf(c_106,plain,
( X0 != sK2
| X1 != sK3
| set_intersection2(X0,X1) = X0 ),
inference(resolution_lifted,[status(thm)],[c_57,c_58]) ).
cnf(c_107,plain,
set_intersection2(sK2,sK3) = sK2,
inference(unflattening,[status(thm)],[c_106]) ).
cnf(c_175,plain,
set_intersection2(cartesian_product2(sK2,X0),cartesian_product2(sK3,X1)) = cartesian_product2(sK2,set_intersection2(X0,X1)),
inference(superposition,[status(thm)],[c_107,c_54]) ).
cnf(c_181,plain,
cartesian_product2(sK2,set_intersection2(sK5,sK4)) != cartesian_product2(sK2,sK4),
inference(demodulation,[status(thm)],[c_55,c_175]) ).
cnf(c_182,plain,
cartesian_product2(sK2,sK4) != cartesian_product2(sK2,sK4),
inference(demodulation,[status(thm)],[c_181,c_49,c_102]) ).
cnf(c_183,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 11:58:42 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.87/1.15 % SZS status Started for theBenchmark.p
% 1.87/1.15 % SZS status Theorem for theBenchmark.p
% 1.87/1.15
% 1.87/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.87/1.15
% 1.87/1.15 ------ iProver source info
% 1.87/1.15
% 1.87/1.15 git: date: 2023-05-31 18:12:56 +0000
% 1.87/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.87/1.15 git: non_committed_changes: false
% 1.87/1.15 git: last_make_outside_of_git: false
% 1.87/1.15
% 1.87/1.15 ------ Parsing...
% 1.87/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.87/1.15
% 1.87/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 1.87/1.15
% 1.87/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.87/1.15
% 1.87/1.15 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.87/1.15 ------ Proving...
% 1.87/1.15 ------ Problem Properties
% 1.87/1.15
% 1.87/1.15
% 1.87/1.15 clauses 7
% 1.87/1.15 conjectures 1
% 1.87/1.15 EPR 1
% 1.87/1.15 Horn 7
% 1.87/1.15 unary 7
% 1.87/1.15 binary 0
% 1.87/1.15 lits 7
% 1.87/1.15 lits eq 7
% 1.87/1.15 fd_pure 0
% 1.87/1.15 fd_pseudo 0
% 1.87/1.15 fd_cond 0
% 1.87/1.15 fd_pseudo_cond 0
% 1.87/1.15 AC symbols 0
% 1.87/1.15
% 1.87/1.15 ------ Schedule UEQ
% 1.87/1.15
% 1.87/1.15 ------ Option_UEQ Time Limit: 10.
% 1.87/1.15
% 1.87/1.15
% 1.87/1.15 ------
% 1.87/1.15 Current options:
% 1.87/1.15 ------
% 1.87/1.15
% 1.87/1.15
% 1.87/1.15
% 1.87/1.15
% 1.87/1.15 ------ Proving...
% 1.87/1.15
% 1.87/1.15
% 1.87/1.15 % SZS status Theorem for theBenchmark.p
% 1.87/1.15
% 1.87/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.87/1.15
% 1.87/1.15
%------------------------------------------------------------------------------