TSTP Solution File: GRP774+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRP774+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n023.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 01:01:46 EDT 2023
% Result : Theorem 7.25s 1.67s
% Output : CNFRefutation 7.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 73 ( 48 unt; 0 def)
% Number of atoms : 126 ( 83 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 94 ( 41 ~; 28 |; 19 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 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 : 122 ( 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_106,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_107,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_106]) ).
cnf(c_114,plain,
( X0 != sK2
| X1 != sK3
| product(X0,product(X1,X0)) = X0 ),
inference(resolution_lifted,[status(thm)],[c_53,c_55]) ).
cnf(c_115,plain,
product(sK2,product(sK3,sK2)) = sK2,
inference(unflattening,[status(thm)],[c_114]) ).
cnf(c_119,plain,
( X0 != sK2
| X1 != sK3
| product(X1,product(X0,X1)) = X1 ),
inference(resolution_lifted,[status(thm)],[c_52,c_55]) ).
cnf(c_120,plain,
product(sK3,product(sK2,sK3)) = sK3,
inference(unflattening,[status(thm)],[c_119]) ).
cnf(c_124,plain,
( X0 != sK0
| X1 != sK1
| product(X0,product(X1,X0)) = X0 ),
inference(resolution_lifted,[status(thm)],[c_53,c_56]) ).
cnf(c_125,plain,
product(sK0,product(sK1,sK0)) = sK0,
inference(unflattening,[status(thm)],[c_124]) ).
cnf(c_129,plain,
( X0 != sK0
| X1 != sK1
| product(X1,product(X0,X1)) = X1 ),
inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).
cnf(c_130,plain,
product(sK1,product(sK0,sK1)) = sK1,
inference(unflattening,[status(thm)],[c_129]) ).
cnf(c_207,plain,
product(X0,product(X0,X1)) = product(X0,X1),
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_208,plain,
product(sK2,product(product(sK3,sK2),X0)) = product(sK2,X0),
inference(superposition,[status(thm)],[c_115,c_49]) ).
cnf(c_209,plain,
product(sK3,product(product(sK2,sK3),X0)) = product(sK3,X0),
inference(superposition,[status(thm)],[c_120,c_49]) ).
cnf(c_210,plain,
product(sK0,product(product(sK1,sK0),X0)) = product(sK0,X0),
inference(superposition,[status(thm)],[c_125,c_49]) ).
cnf(c_211,plain,
product(sK1,product(product(sK0,sK1),X0)) = product(sK1,X0),
inference(superposition,[status(thm)],[c_130,c_49]) ).
cnf(c_213,plain,
product(X0,product(X1,product(X0,X1))) = product(X0,X1),
inference(superposition,[status(thm)],[c_49,c_50]) ).
cnf(c_229,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_107,c_49]) ).
cnf(c_235,plain,
product(product(X0,X1),product(X0,product(X1,X2))) = product(X0,product(X1,X2)),
inference(superposition,[status(thm)],[c_49,c_207]) ).
cnf(c_254,plain,
product(sK1,product(sK0,product(sK1,X0))) = product(sK1,X0),
inference(demodulation,[status(thm)],[c_211,c_49]) ).
cnf(c_261,plain,
product(sK0,product(sK1,product(sK0,X0))) = product(sK0,X0),
inference(demodulation,[status(thm)],[c_210,c_49]) ).
cnf(c_267,plain,
product(sK3,product(sK2,product(sK3,X0))) = product(sK3,X0),
inference(demodulation,[status(thm)],[c_209,c_49]) ).
cnf(c_287,plain,
product(sK2,product(sK3,product(sK2,X0))) = product(sK2,X0),
inference(demodulation,[status(thm)],[c_208,c_49]) ).
cnf(c_304,plain,
product(X0,product(X1,product(X2,product(X0,product(X1,X2))))) = product(X0,product(X1,X2)),
inference(superposition,[status(thm)],[c_49,c_213]) ).
cnf(c_340,plain,
product(X0,product(X1,product(X0,product(X1,X2)))) = product(X0,product(X1,X2)),
inference(demodulation,[status(thm)],[c_235,c_49]) ).
cnf(c_346,plain,
product(X0,product(product(X1,X2),product(X0,product(X1,product(X2,X3))))) = product(X0,product(X1,product(X2,X3))),
inference(superposition,[status(thm)],[c_49,c_340]) ).
cnf(c_472,plain,
product(sK1,product(X0,product(sK0,product(sK1,X0)))) = product(sK1,product(sK0,product(sK1,X0))),
inference(superposition,[status(thm)],[c_304,c_254]) ).
cnf(c_474,plain,
product(sK0,product(X0,product(sK1,product(sK0,X0)))) = product(sK0,product(sK1,product(sK0,X0))),
inference(superposition,[status(thm)],[c_304,c_261]) ).
cnf(c_567,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_346,c_49]) ).
cnf(c_601,plain,
product(X0,product(sK2,product(sK3,product(X0,sK2)))) = product(X0,sK2),
inference(superposition,[status(thm)],[c_115,c_567]) ).
cnf(c_610,plain,
product(X0,product(sK2,product(sK3,product(X0,product(sK2,X1))))) = product(X0,product(sK2,X1)),
inference(superposition,[status(thm)],[c_287,c_567]) ).
cnf(c_614,plain,
product(X0,product(X1,product(product(X2,X3),product(X0,product(X1,product(X2,product(X3,X4))))))) = product(X0,product(X1,product(X2,product(X3,X4)))),
inference(superposition,[status(thm)],[c_49,c_567]) ).
cnf(c_647,plain,
product(sK3,product(X0,product(sK2,product(sK3,product(X0,X1))))) = product(sK3,product(sK2,product(sK3,product(X0,X1)))),
inference(superposition,[status(thm)],[c_567,c_267]) ).
cnf(c_657,plain,
product(sK0,product(sK2,product(sK3,product(sK0,sK2)))) = product(sK0,sK2),
inference(instantiation,[status(thm)],[c_601]) ).
cnf(c_890,plain,
product(sK0,product(X0,product(sK1,product(sK0,X0)))) = product(sK0,X0),
inference(demodulation,[status(thm)],[c_474,c_261]) ).
cnf(c_939,plain,
product(sK1,product(X0,product(sK0,product(sK1,X0)))) = product(sK1,X0),
inference(demodulation,[status(thm)],[c_472,c_254]) ).
cnf(c_2583,plain,
product(sK3,product(X0,product(sK2,product(sK3,product(X0,X1))))) = product(sK3,product(X0,X1)),
inference(demodulation,[status(thm)],[c_647,c_267]) ).
cnf(c_3070,plain,
product(X0,product(X1,product(X2,product(X3,product(X0,product(X1,product(X2,product(X3,X4)))))))) = product(X0,product(X1,product(X2,product(X3,X4)))),
inference(demodulation,[status(thm)],[c_614,c_49]) ).
cnf(c_3178,plain,
product(X0,product(sK0,product(X1,product(sK1,product(X0,product(sK0,X1)))))) = product(X0,product(sK0,X1)),
inference(superposition,[status(thm)],[c_890,c_3070]) ).
cnf(c_3192,plain,
product(X0,product(sK3,product(X1,product(sK2,product(X0,product(sK3,product(X1,X2))))))) = product(X0,product(sK3,product(X1,X2))),
inference(superposition,[status(thm)],[c_2583,c_3070]) ).
cnf(c_15657,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_3178,c_610]) ).
cnf(c_15670,plain,
( product(sK1,product(sK3,product(sK0,product(sK2,product(sK1,sK3))))) != product(sK1,sK3)
| product(sK0,product(sK2,product(sK3,product(sK0,sK2)))) != product(sK0,sK2) ),
inference(demodulation,[status(thm)],[c_229,c_15657]) ).
cnf(c_16535,plain,
product(sK1,product(sK3,product(sK0,product(sK2,product(sK1,sK3))))) = product(sK1,sK3),
inference(superposition,[status(thm)],[c_939,c_3192]) ).
cnf(c_16794,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16535,c_15670,c_657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP774+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 20:00:40 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.25/1.67 % SZS status Started for theBenchmark.p
% 7.25/1.67 % SZS status Theorem for theBenchmark.p
% 7.25/1.67
% 7.25/1.67 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.25/1.67
% 7.25/1.67 ------ iProver source info
% 7.25/1.67
% 7.25/1.67 git: date: 2023-05-31 18:12:56 +0000
% 7.25/1.67 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.25/1.67 git: non_committed_changes: false
% 7.25/1.67 git: last_make_outside_of_git: false
% 7.25/1.67
% 7.25/1.67 ------ Parsing...
% 7.25/1.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.25/1.67
% 7.25/1.67 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e
% 7.25/1.67
% 7.25/1.67 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.25/1.67
% 7.25/1.67 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.25/1.67 ------ Proving...
% 7.25/1.67 ------ Problem Properties
% 7.25/1.67
% 7.25/1.67
% 7.25/1.67 clauses 9
% 7.25/1.67 conjectures 0
% 7.25/1.67 EPR 0
% 7.25/1.67 Horn 9
% 7.25/1.67 unary 6
% 7.25/1.67 binary 3
% 7.25/1.67 lits 12
% 7.25/1.67 lits eq 12
% 7.25/1.67 fd_pure 0
% 7.25/1.67 fd_pseudo 0
% 7.25/1.67 fd_cond 0
% 7.25/1.67 fd_pseudo_cond 0
% 7.25/1.67 AC symbols 0
% 7.25/1.67
% 7.25/1.67 ------ Input Options Time Limit: Unbounded
% 7.25/1.67
% 7.25/1.67
% 7.25/1.67 ------
% 7.25/1.67 Current options:
% 7.25/1.67 ------
% 7.25/1.67
% 7.25/1.67
% 7.25/1.67
% 7.25/1.67
% 7.25/1.67 ------ Proving...
% 7.25/1.67
% 7.25/1.67
% 7.25/1.67 % SZS status Theorem for theBenchmark.p
% 7.25/1.67
% 7.25/1.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.25/1.67
% 7.25/1.67
%------------------------------------------------------------------------------