TSTP Solution File: GRP001+6 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.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 00:56:30 EDT 2023
% Result : Theorem 3.60s 1.12s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 52 ( 18 unt; 0 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 309 ( 109 ~; 96 |; 86 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 297 ( 1 sgn; 200 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f3,plain,
~ ! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X2] : product(X2,inverse(X2),X0)
& ! [X3] : product(X0,X3,X3)
& ! [X4] : product(X4,X0,X4)
& ! [X5,X6,X7,X8,X9,X10] :
( ( product(X5,X9,X10)
& product(X6,X7,X9)
& product(X5,X6,X8) )
=> product(X8,X7,X10) )
& ! [X11,X12,X13,X14,X15,X16] :
( ( product(X14,X13,X16)
& product(X12,X13,X15)
& product(X11,X12,X14) )
=> product(X11,X15,X16) )
& ! [X17,X18] :
? [X19] : product(X17,X18,X19) )
=> ( ! [X20] : product(X20,X20,X0)
=> ! [X21,X22,X23] :
( product(X21,X22,X23)
=> product(X22,X21,X23) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ? [X21,X22,X23] :
( ~ product(X22,X21,X23)
& product(X21,X22,X23) )
& ! [X20] : product(X20,X20,X0)
& ! [X1] : product(inverse(X1),X1,X0)
& ! [X2] : product(X2,inverse(X2),X0)
& ! [X3] : product(X0,X3,X3)
& ! [X4] : product(X4,X0,X4)
& ! [X5,X6,X7,X8,X9,X10] :
( product(X8,X7,X10)
| ~ product(X5,X9,X10)
| ~ product(X6,X7,X9)
| ~ product(X5,X6,X8) )
& ! [X11,X12,X13,X14,X15,X16] :
( product(X11,X15,X16)
| ~ product(X14,X13,X16)
| ~ product(X12,X13,X15)
| ~ product(X11,X12,X14) )
& ! [X17,X18] :
? [X19] : product(X17,X18,X19) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
( ? [X21,X22,X23] :
( ~ product(X22,X21,X23)
& product(X21,X22,X23) )
& ! [X20] : product(X20,X20,X0)
& ! [X1] : product(inverse(X1),X1,X0)
& ! [X2] : product(X2,inverse(X2),X0)
& ! [X3] : product(X0,X3,X3)
& ! [X4] : product(X4,X0,X4)
& ! [X5,X6,X7,X8,X9,X10] :
( product(X8,X7,X10)
| ~ product(X5,X9,X10)
| ~ product(X6,X7,X9)
| ~ product(X5,X6,X8) )
& ! [X11,X12,X13,X14,X15,X16] :
( product(X11,X15,X16)
| ~ product(X14,X13,X16)
| ~ product(X12,X13,X15)
| ~ product(X11,X12,X14) )
& ! [X17,X18] :
? [X19] : product(X17,X18,X19) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
& ! [X4] : product(X4,X4,X0)
& ! [X5] : product(inverse(X5),X5,X0)
& ! [X6] : product(X6,inverse(X6),X0)
& ! [X7] : product(X0,X7,X7)
& ! [X8] : product(X8,X0,X8)
& ! [X9,X10,X11,X12,X13,X14] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
& ! [X15,X16,X17,X18,X19,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) )
& ! [X21,X22] :
? [X23] : product(X21,X22,X23) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ? [X0] :
( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
& ! [X4] : product(X4,X4,X0)
& ! [X5] : product(inverse(X5),X5,X0)
& ! [X6] : product(X6,inverse(X6),X0)
& ! [X7] : product(X0,X7,X7)
& ! [X8] : product(X8,X0,X8)
& ! [X9,X10,X11,X12,X13,X14] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
& ! [X15,X16,X17,X18,X19,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) )
& ! [X21,X22] :
? [X23] : product(X21,X22,X23) )
=> ( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
& ! [X4] : product(X4,X4,sK0)
& ! [X5] : product(inverse(X5),X5,sK0)
& ! [X6] : product(X6,inverse(X6),sK0)
& ! [X7] : product(sK0,X7,X7)
& ! [X8] : product(X8,sK0,X8)
& ! [X9,X10,X11,X12,X13,X14] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
& ! [X15,X16,X17,X18,X19,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) )
& ! [X21,X22] :
? [X23] : product(X21,X22,X23) ) ),
introduced(choice_axiom,[]) ).
fof(f8,plain,
( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
=> ( ~ product(sK2,sK1,sK3)
& product(sK1,sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
! [X21,X22] :
( ? [X23] : product(X21,X22,X23)
=> product(X21,X22,sK4(X21,X22)) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
( ~ product(sK2,sK1,sK3)
& product(sK1,sK2,sK3)
& ! [X4] : product(X4,X4,sK0)
& ! [X5] : product(inverse(X5),X5,sK0)
& ! [X6] : product(X6,inverse(X6),sK0)
& ! [X7] : product(sK0,X7,X7)
& ! [X8] : product(X8,sK0,X8)
& ! [X9,X10,X11,X12,X13,X14] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
& ! [X15,X16,X17,X18,X19,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) )
& ! [X21,X22] : product(X21,X22,sK4(X21,X22)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f6,f9,f8,f7]) ).
fof(f12,plain,
! [X18,X19,X16,X17,X15,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) ),
inference(cnf_transformation,[],[f10]) ).
fof(f13,plain,
! [X10,X11,X9,X14,X12,X13] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) ),
inference(cnf_transformation,[],[f10]) ).
fof(f14,plain,
! [X8] : product(X8,sK0,X8),
inference(cnf_transformation,[],[f10]) ).
fof(f15,plain,
! [X7] : product(sK0,X7,X7),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X4] : product(X4,X4,sK0),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
product(sK1,sK2,sK3),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
~ product(sK2,sK1,sK3),
inference(cnf_transformation,[],[f10]) ).
cnf(c_49,negated_conjecture,
~ product(sK2,sK1,sK3),
inference(cnf_transformation,[],[f20]) ).
cnf(c_50,negated_conjecture,
product(sK1,sK2,sK3),
inference(cnf_transformation,[],[f19]) ).
cnf(c_51,negated_conjecture,
product(X0,X0,sK0),
inference(cnf_transformation,[],[f18]) ).
cnf(c_54,negated_conjecture,
product(sK0,X0,X0),
inference(cnf_transformation,[],[f15]) ).
cnf(c_55,negated_conjecture,
product(X0,sK0,X0),
inference(cnf_transformation,[],[f14]) ).
cnf(c_56,negated_conjecture,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| product(X4,X5,X2) ),
inference(cnf_transformation,[],[f13]) ).
cnf(c_57,negated_conjecture,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X4)
| product(X0,X5,X4) ),
inference(cnf_transformation,[],[f12]) ).
cnf(c_95,plain,
( ~ product(X0,X1,sK3)
| ~ product(X0,X2,sK2)
| ~ product(X2,sK1,X1)
| product(sK2,sK1,sK3) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_99,plain,
( ~ product(X0,sK1,sK2)
| ~ product(sK1,X0,sK2)
| ~ product(sK1,sK2,sK3)
| product(sK2,sK1,sK3) ),
inference(instantiation,[status(thm)],[c_95]) ).
cnf(c_102,plain,
product(sK0,sK3,sK3),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_113,plain,
product(sK1,sK0,sK1),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_115,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,sK1)
| product(X2,X3,sK1) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_169,plain,
( ~ product(X0,X1,sK0)
| ~ product(sK1,X0,X2)
| ~ product(sK1,sK0,sK1)
| product(X2,X1,sK1) ),
inference(instantiation,[status(thm)],[c_115]) ).
cnf(c_189,plain,
product(sK0,sK2,sK2),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_195,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,sK2)
| product(X0,X4,sK2) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_200,plain,
( ~ product(X0,X1,sK2)
| ~ product(sK1,X0,X2)
| product(X2,X1,sK3) ),
inference(superposition,[status(thm)],[c_50,c_56]) ).
cnf(c_322,plain,
product(sK3,sK3,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_345,plain,
( ~ product(X0,X1,X2)
| ~ product(X2,X3,X4)
| ~ product(X1,X3,sK3)
| product(X0,sK3,X4) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_445,plain,
( ~ product(sK2,X0,sK0)
| ~ product(sK1,sK2,sK3)
| ~ product(sK1,sK0,sK1)
| product(sK3,X0,sK1) ),
inference(instantiation,[status(thm)],[c_169]) ).
cnf(c_576,plain,
( ~ product(sK1,sK2,X0)
| product(X0,sK0,sK3) ),
inference(superposition,[status(thm)],[c_55,c_200]) ).
cnf(c_595,plain,
( ~ product(sK2,sK2,sK0)
| ~ product(sK1,sK2,sK3)
| ~ product(sK1,sK0,sK1)
| product(sK3,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_445]) ).
cnf(c_596,plain,
product(sK2,sK2,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_861,plain,
( ~ product(X0,X1,sK0)
| ~ product(X1,sK2,X2)
| ~ product(sK0,sK2,sK2)
| product(X0,X2,sK2) ),
inference(instantiation,[status(thm)],[c_195]) ).
cnf(c_1025,plain,
( ~ product(X0,sK0,X1)
| ~ product(X1,sK3,X2)
| ~ product(sK0,sK3,sK3)
| product(X0,sK3,X2) ),
inference(instantiation,[status(thm)],[c_345]) ).
cnf(c_3044,plain,
( ~ product(X0,X1,X2)
| ~ product(sK0,X1,X3)
| product(X0,X2,X3) ),
inference(superposition,[status(thm)],[c_51,c_57]) ).
cnf(c_3047,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| product(sK0,X2,X3) ),
inference(superposition,[status(thm)],[c_54,c_57]) ).
cnf(c_3048,plain,
( ~ product(X0,X1,X2)
| ~ product(sK0,X1,X3)
| product(X0,X3,X2) ),
inference(superposition,[status(thm)],[c_55,c_57]) ).
cnf(c_3154,plain,
( ~ product(sK0,sK2,X0)
| product(sK1,sK3,X0) ),
inference(superposition,[status(thm)],[c_50,c_3044]) ).
cnf(c_3183,plain,
( ~ product(sK1,sK2,X0)
| product(sK0,sK3,X0) ),
inference(superposition,[status(thm)],[c_50,c_3047]) ).
cnf(c_4351,plain,
product(sK1,sK3,sK2),
inference(superposition,[status(thm)],[c_54,c_3154]) ).
cnf(c_4463,plain,
( ~ product(sK0,sK3,X0)
| product(sK1,X0,sK2) ),
inference(superposition,[status(thm)],[c_4351,c_3048]) ).
cnf(c_4835,plain,
( ~ product(X0,sK3,sK0)
| ~ product(sK3,sK2,sK1)
| ~ product(sK0,sK2,sK2)
| product(X0,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_861]) ).
cnf(c_5573,plain,
( ~ product(X0,sK0,sK3)
| ~ product(sK3,sK3,sK0)
| ~ product(sK0,sK3,sK3)
| product(X0,sK3,sK0) ),
inference(instantiation,[status(thm)],[c_1025]) ).
cnf(c_6042,plain,
~ product(sK1,sK2,X0),
inference(global_subsumption_just,[status(thm)],[c_3183,c_50,c_49,c_99,c_102,c_113,c_189,c_322,c_576,c_595,c_596,c_3183,c_4463,c_4835,c_5573]) ).
cnf(c_6045,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_6042]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n012.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 21:39:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.60/1.12 % SZS status Started for theBenchmark.p
% 3.60/1.12 % SZS status Theorem for theBenchmark.p
% 3.60/1.12
% 3.60/1.12 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.60/1.12
% 3.60/1.12 ------ iProver source info
% 3.60/1.12
% 3.60/1.12 git: date: 2023-05-31 18:12:56 +0000
% 3.60/1.12 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.60/1.12 git: non_committed_changes: false
% 3.60/1.12 git: last_make_outside_of_git: false
% 3.60/1.12
% 3.60/1.12 ------ Parsing...
% 3.60/1.12 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.60/1.12
% 3.60/1.12 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 3.60/1.12
% 3.60/1.12 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.60/1.12 ------ Proving...
% 3.60/1.12 ------ Problem Properties
% 3.60/1.12
% 3.60/1.12
% 3.60/1.12 clauses 10
% 3.60/1.12 conjectures 10
% 3.60/1.12 EPR 7
% 3.60/1.12 Horn 10
% 3.60/1.12 unary 8
% 3.60/1.12 binary 0
% 3.60/1.12 lits 16
% 3.60/1.12 lits eq 0
% 3.60/1.12 fd_pure 0
% 3.60/1.12 fd_pseudo 0
% 3.60/1.12 fd_cond 0
% 3.60/1.12 fd_pseudo_cond 0
% 3.60/1.12 AC symbols 0
% 3.60/1.12
% 3.60/1.12 ------ Schedule dynamic 5 is on
% 3.60/1.12
% 3.60/1.12 ------ no equalities: superposition off
% 3.60/1.12
% 3.60/1.12 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 3.60/1.12
% 3.60/1.12 ------
% 3.60/1.12 Current options:
% 3.60/1.12 ------
% 3.60/1.12
% 3.60/1.12
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% 3.60/1.12
% 3.60/1.12 ------ Proving...
% 3.60/1.12
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% 3.60/1.12 % SZS status Theorem for theBenchmark.p
% 3.60/1.12
% 3.60/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 3.60/1.12
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