TSTP Solution File: GRP774+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRP774+1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 : Mon Jun 24 07:02:09 EDT 2024
% Result : Theorem 8.32s 1.70s
% Output : CNFRefutation 8.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 79 ( 50 unt; 0 def)
% Number of atoms : 136 ( 89 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 102 ( 45 ~; 32 |; 19 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 35 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : product(product(X2,X1),X0) = product(X2,product(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
fof(f2,axiom,
! [X2] : product(X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
fof(f3,axiom,
! [X3,X4] :
( d(X3,X4)
<=> ( product(X4,product(X3,X4)) = X4
& product(X3,product(X4,X3)) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(f4,conjecture,
! [X5,X6,X7,X8] :
( ( d(X7,X8)
& d(X5,X6) )
=> d(product(X5,X7),product(X6,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f5,negated_conjecture,
~ ! [X5,X6,X7,X8] :
( ( d(X7,X8)
& d(X5,X6) )
=> d(product(X5,X7),product(X6,X8)) ),
inference(negated_conjecture,[],[f4]) ).
fof(f6,plain,
! [X0] : product(X0,X0) = X0,
inference(rectify,[],[f2]) ).
fof(f7,plain,
! [X0,X1] :
( d(X0,X1)
<=> ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) ),
inference(rectify,[],[f3]) ).
fof(f8,plain,
~ ! [X0,X1,X2,X3] :
( ( d(X2,X3)
& d(X0,X1) )
=> d(product(X0,X2),product(X1,X3)) ),
inference(rectify,[],[f5]) ).
fof(f9,plain,
? [X0,X1,X2,X3] :
( ~ d(product(X0,X2),product(X1,X3))
& d(X2,X3)
& d(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f10,plain,
? [X0,X1,X2,X3] :
( ~ d(product(X0,X2),product(X1,X3))
& d(X2,X3)
& d(X0,X1) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( d(X0,X1)
| product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0 )
& ( ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 )
| ~ d(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( ( d(X0,X1)
| product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0 )
& ( ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 )
| ~ d(X0,X1) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
( ? [X0,X1,X2,X3] :
( ~ d(product(X0,X2),product(X1,X3))
& d(X2,X3)
& d(X0,X1) )
=> ( ~ d(product(sK0,sK2),product(sK1,sK3))
& d(sK2,sK3)
& d(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ~ d(product(sK0,sK2),product(sK1,sK3))
& d(sK2,sK3)
& d(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f13]) ).
fof(f15,plain,
! [X2,X0,X1] : product(product(X2,X1),X0) = product(X2,product(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f17,plain,
! [X0,X1] :
( product(X0,product(X1,X0)) = X0
| ~ d(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0,X1] :
( product(X1,product(X0,X1)) = X1
| ~ d(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( d(X0,X1)
| product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
d(sK0,sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
d(sK2,sK3),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
~ d(product(sK0,sK2),product(sK1,sK3)),
inference(cnf_transformation,[],[f14]) ).
cnf(c_49,plain,
product(product(X0,X1),X2) = product(X0,product(X1,X2)),
inference(cnf_transformation,[],[f15]) ).
cnf(c_50,plain,
product(X0,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
cnf(c_51,plain,
( product(X0,product(X1,X0)) != X0
| product(X1,product(X0,X1)) != X1
| d(X1,X0) ),
inference(cnf_transformation,[],[f19]) ).
cnf(c_52,plain,
( ~ d(X0,X1)
| product(X1,product(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f18]) ).
cnf(c_53,plain,
( ~ d(X0,X1)
| product(X0,product(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f17]) ).
cnf(c_54,negated_conjecture,
~ d(product(sK0,sK2),product(sK1,sK3)),
inference(cnf_transformation,[],[f22]) ).
cnf(c_55,negated_conjecture,
d(sK2,sK3),
inference(cnf_transformation,[],[f21]) ).
cnf(c_56,negated_conjecture,
d(sK0,sK1),
inference(cnf_transformation,[],[f20]) ).
cnf(c_61,plain,
( product(X0,product(X1,X0)) = X0
| ~ d(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
cnf(c_62,plain,
( ~ d(X0,X1)
| product(X0,product(X1,X0)) = X0 ),
inference(renaming,[status(thm)],[c_61]) ).
cnf(c_63,plain,
( product(X1,product(X0,X1)) = X1
| ~ d(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
cnf(c_64,plain,
( ~ d(X0,X1)
| product(X1,product(X0,X1)) = X1 ),
inference(renaming,[status(thm)],[c_63]) ).
cnf(c_73,plain,
( product(X0,product(X1,X0)) != X0
| product(X1,product(X0,X1)) != X1
| product(sK0,sK2) != X1
| product(sK1,sK3) != X0 ),
inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).
cnf(c_74,plain,
( product(product(sK0,sK2),product(product(sK1,sK3),product(sK0,sK2))) != product(sK0,sK2)
| product(product(sK1,sK3),product(product(sK0,sK2),product(sK1,sK3))) != product(sK1,sK3) ),
inference(unflattening,[status(thm)],[c_73]) ).
cnf(c_81,plain,
( X0 != sK2
| X1 != sK3
| product(X0,product(X1,X0)) = X0 ),
inference(resolution_lifted,[status(thm)],[c_62,c_55]) ).
cnf(c_82,plain,
product(sK2,product(sK3,sK2)) = sK2,
inference(unflattening,[status(thm)],[c_81]) ).
cnf(c_86,plain,
( X0 != sK2
| X1 != sK3
| product(X1,product(X0,X1)) = X1 ),
inference(resolution_lifted,[status(thm)],[c_64,c_55]) ).
cnf(c_87,plain,
product(sK3,product(sK2,sK3)) = sK3,
inference(unflattening,[status(thm)],[c_86]) ).
cnf(c_91,plain,
( X0 != sK0
| X1 != sK1
| product(X0,product(X1,X0)) = X0 ),
inference(resolution_lifted,[status(thm)],[c_62,c_56]) ).
cnf(c_92,plain,
product(sK0,product(sK1,sK0)) = sK0,
inference(unflattening,[status(thm)],[c_91]) ).
cnf(c_96,plain,
( X0 != sK0
| X1 != sK1
| product(X1,product(X0,X1)) = X1 ),
inference(resolution_lifted,[status(thm)],[c_64,c_56]) ).
cnf(c_97,plain,
product(sK1,product(sK0,sK1)) = sK1,
inference(unflattening,[status(thm)],[c_96]) ).
cnf(c_151,plain,
( product(product(sK0,sK2),product(product(sK1,sK3),product(sK0,sK2))) != product(sK0,sK2)
| product(product(sK1,sK3),product(sK0,product(sK2,product(sK1,sK3)))) != product(sK1,sK3) ),
inference(demodulation,[status(thm)],[c_74,c_49]) ).
cnf(c_154,plain,
( product(sK0,product(sK2,product(sK1,product(sK3,product(sK0,sK2))))) != product(sK0,sK2)
| product(sK1,product(sK3,product(sK0,product(sK2,product(sK1,sK3))))) != product(sK1,sK3) ),
inference(demodulation,[status(thm)],[c_151,c_49]) ).
cnf(c_159,plain,
product(X0,product(X0,X1)) = product(X0,X1),
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_160,plain,
product(sK2,product(product(sK3,sK2),X0)) = product(sK2,X0),
inference(superposition,[status(thm)],[c_82,c_49]) ).
cnf(c_161,plain,
product(sK3,product(product(sK2,sK3),X0)) = product(sK3,X0),
inference(superposition,[status(thm)],[c_87,c_49]) ).
cnf(c_162,plain,
product(sK0,product(product(sK1,sK0),X0)) = product(sK0,X0),
inference(superposition,[status(thm)],[c_92,c_49]) ).
cnf(c_163,plain,
product(sK1,product(product(sK0,sK1),X0)) = product(sK1,X0),
inference(superposition,[status(thm)],[c_97,c_49]) ).
cnf(c_165,plain,
product(X0,product(X1,product(X0,X1))) = product(X0,X1),
inference(superposition,[status(thm)],[c_49,c_50]) ).
cnf(c_166,plain,
product(sK1,product(sK0,product(sK1,X0))) = product(sK1,X0),
inference(demodulation,[status(thm)],[c_163,c_49]) ).
cnf(c_167,plain,
product(sK0,product(sK1,product(sK0,X0))) = product(sK0,X0),
inference(demodulation,[status(thm)],[c_162,c_49]) ).
cnf(c_168,plain,
product(sK3,product(sK2,product(sK3,X0))) = product(sK3,X0),
inference(demodulation,[status(thm)],[c_161,c_49]) ).
cnf(c_169,plain,
product(sK2,product(sK3,product(sK2,X0))) = product(sK2,X0),
inference(demodulation,[status(thm)],[c_160,c_49]) ).
cnf(c_189,plain,
product(X0,product(X1,product(product(X0,X1),X2))) = product(product(X0,X1),X2),
inference(superposition,[status(thm)],[c_159,c_49]) ).
cnf(c_190,plain,
product(X0,product(X1,product(X0,product(X1,X2)))) = product(X0,product(X1,X2)),
inference(demodulation,[status(thm)],[c_189,c_49]) ).
cnf(c_226,plain,
product(X0,product(X1,product(X2,product(product(X0,X1),X2)))) = product(product(X0,X1),X2),
inference(superposition,[status(thm)],[c_165,c_49]) ).
cnf(c_232,plain,
product(X0,product(X1,product(X2,product(X0,product(X1,X2))))) = product(X0,product(X1,X2)),
inference(demodulation,[status(thm)],[c_226,c_49]) ).
cnf(c_256,plain,
product(X0,product(X1,product(X2,product(product(X0,X1),product(X2,X3))))) = product(product(X0,X1),product(X2,X3)),
inference(superposition,[status(thm)],[c_190,c_49]) ).
cnf(c_263,plain,
product(X0,product(X1,product(X2,product(X0,product(X1,product(X2,X3)))))) = product(X0,product(X1,product(X2,X3))),
inference(demodulation,[status(thm)],[c_256,c_49]) ).
cnf(c_321,plain,
product(X0,product(X1,product(X2,product(X3,product(product(X0,X1),product(X2,X3)))))) = product(product(X0,X1),product(X2,X3)),
inference(superposition,[status(thm)],[c_232,c_49]) ).
cnf(c_345,plain,
product(X0,product(X1,product(X2,product(X3,product(X0,product(X1,product(X2,X3))))))) = product(X0,product(X1,product(X2,X3))),
inference(demodulation,[status(thm)],[c_321,c_49]) ).
cnf(c_389,plain,
product(X0,product(sK2,product(sK3,product(X0,sK2)))) = product(X0,sK2),
inference(superposition,[status(thm)],[c_82,c_263]) ).
cnf(c_390,plain,
product(X0,product(sK3,product(sK2,product(X0,sK3)))) = product(X0,sK3),
inference(superposition,[status(thm)],[c_87,c_263]) ).
cnf(c_395,plain,
product(X0,product(sK1,product(sK0,product(X0,product(sK1,X1))))) = product(X0,product(sK1,X1)),
inference(superposition,[status(thm)],[c_166,c_263]) ).
cnf(c_396,plain,
product(X0,product(sK0,product(sK1,product(X0,product(sK0,X1))))) = product(X0,product(sK0,X1)),
inference(superposition,[status(thm)],[c_167,c_263]) ).
cnf(c_397,plain,
product(X0,product(sK3,product(sK2,product(X0,product(sK3,X1))))) = product(X0,product(sK3,X1)),
inference(superposition,[status(thm)],[c_168,c_263]) ).
cnf(c_398,plain,
product(X0,product(sK2,product(sK3,product(X0,product(sK2,X1))))) = product(X0,product(sK2,X1)),
inference(superposition,[status(thm)],[c_169,c_263]) ).
cnf(c_1630,plain,
product(X0,product(sK0,product(X1,product(sK1,product(X0,product(sK0,X1)))))) = product(X0,product(sK0,product(sK1,product(X0,product(sK0,X1))))),
inference(superposition,[status(thm)],[c_345,c_396]) ).
cnf(c_1706,plain,
product(X0,product(sK0,product(X1,product(sK1,product(X0,product(sK0,X1)))))) = product(X0,product(sK0,X1)),
inference(demodulation,[status(thm)],[c_1630,c_396]) ).
cnf(c_1746,plain,
product(X0,product(sK1,product(X1,product(sK0,product(X0,product(sK1,X1)))))) = product(X0,product(sK1,product(sK0,product(X0,product(sK1,X1))))),
inference(superposition,[status(thm)],[c_345,c_395]) ).
cnf(c_1824,plain,
product(X0,product(sK1,product(X1,product(sK0,product(X0,product(sK1,X1)))))) = product(X0,product(sK1,X1)),
inference(demodulation,[status(thm)],[c_1746,c_395]) ).
cnf(c_8401,plain,
product(sK0,product(sK2,product(sK1,product(sK3,product(sK0,sK2))))) = product(sK0,product(sK2,product(sK3,product(sK0,sK2)))),
inference(superposition,[status(thm)],[c_1706,c_398]) ).
cnf(c_8420,plain,
product(sK0,product(sK2,product(sK1,product(sK3,product(sK0,sK2))))) = product(sK0,sK2),
inference(demodulation,[status(thm)],[c_8401,c_389]) ).
cnf(c_9222,plain,
product(sK1,product(sK3,product(sK0,product(sK2,product(sK1,sK3))))) = product(sK1,product(sK3,product(sK2,product(sK1,sK3)))),
inference(superposition,[status(thm)],[c_1824,c_397]) ).
cnf(c_9246,plain,
product(sK1,product(sK3,product(sK0,product(sK2,product(sK1,sK3))))) = product(sK1,sK3),
inference(demodulation,[status(thm)],[c_9222,c_390]) ).
cnf(c_9262,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9246,c_8420,c_154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP774+1 : TPTP v8.2.0. Released v4.1.0.
% 0.08/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n020.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 : Thu Jun 20 06:52:09 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.32/1.70 % SZS status Started for theBenchmark.p
% 8.32/1.70 % SZS status Theorem for theBenchmark.p
% 8.32/1.70
% 8.32/1.70 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 8.32/1.70
% 8.32/1.70 ------ iProver source info
% 8.32/1.70
% 8.32/1.70 git: date: 2024-06-12 09:56:46 +0000
% 8.32/1.70 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 8.32/1.70 git: non_committed_changes: false
% 8.32/1.70
% 8.32/1.70 ------ Parsing...
% 8.32/1.70 ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.32/1.70
% 8.32/1.70 ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe_e
% 8.32/1.70
% 8.32/1.70 ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e
% 8.32/1.70
% 8.32/1.70 ------ Preprocessing...
% 8.32/1.70 ------ Proving...
% 8.32/1.70 ------ Problem Properties
% 8.32/1.70
% 8.32/1.70
% 8.32/1.70 clauses 9
% 8.32/1.70 conjectures 0
% 8.32/1.70 EPR 0
% 8.32/1.70 Horn 9
% 8.32/1.70 unary 6
% 8.32/1.70 binary 3
% 8.32/1.70 lits 12
% 8.32/1.70 lits eq 12
% 8.32/1.70 fd_pure 0
% 8.32/1.70 fd_pseudo 0
% 8.32/1.70 fd_cond 0
% 8.32/1.70 fd_pseudo_cond 0
% 8.32/1.70 AC symbols 0
% 8.32/1.70
% 8.32/1.70 ------ Input Options Time Limit: Unbounded
% 8.32/1.70
% 8.32/1.70
% 8.32/1.70 ------
% 8.32/1.70 Current options:
% 8.32/1.70 ------
% 8.32/1.70
% 8.32/1.70
% 8.32/1.70
% 8.32/1.70
% 8.32/1.70 ------ Proving...
% 8.32/1.70
% 8.32/1.70
% 8.32/1.70 % SZS status Theorem for theBenchmark.p
% 8.32/1.70
% 8.32/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.32/1.70
% 8.32/1.71
%------------------------------------------------------------------------------