TSTP Solution File: GRP012+5 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 : Fri May 3 02:19:46 EDT 2024
% Result : Theorem 3.69s 1.15s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 18 unt; 0 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 243 ( 76 ~; 61 |; 91 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 270 ( 0 sgn 195 !; 37 ?)
% 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) )
=> ! [X4,X5,X6,X1] :
( ( product(X5,X4,X1)
& product(inverse(X4),inverse(X5),X6) )
=> product(inverse(X6),inverse(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distribution) ).
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) )
=> ! [X4,X5,X6,X1] :
( ( product(X5,X4,X1)
& product(inverse(X4),inverse(X5),X6) )
=> product(inverse(X6),inverse(X1),X0) ) ),
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,X21,X22,X23] :
( ( product(X21,X20,X23)
& product(inverse(X20),inverse(X21),X22) )
=> product(inverse(X22),inverse(X23),X0) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ? [X20,X21,X22,X23] :
( ~ product(inverse(X22),inverse(X23),X0)
& product(X21,X20,X23)
& product(inverse(X20),inverse(X21),X22) )
& ! [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] :
( ? [X20,X21,X22,X23] :
( ~ product(inverse(X22),inverse(X23),X0)
& product(X21,X20,X23)
& product(inverse(X20),inverse(X21),X22) )
& ! [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,X4] :
( ~ product(inverse(X3),inverse(X4),X0)
& product(X2,X1,X4)
& product(inverse(X1),inverse(X2),X3) )
& ! [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,X4] :
( ~ product(inverse(X3),inverse(X4),X0)
& product(X2,X1,X4)
& product(inverse(X1),inverse(X2),X3) )
& ! [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) )
=> ( ? [X4,X3,X2,X1] :
( ~ product(inverse(X3),inverse(X4),sK0)
& product(X2,X1,X4)
& product(inverse(X1),inverse(X2),X3) )
& ! [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,
( ? [X4,X3,X2,X1] :
( ~ product(inverse(X3),inverse(X4),sK0)
& product(X2,X1,X4)
& product(inverse(X1),inverse(X2),X3) )
=> ( ~ product(inverse(sK3),inverse(sK4),sK0)
& product(sK2,sK1,sK4)
& product(inverse(sK1),inverse(sK2),sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
! [X21,X22] :
( ? [X23] : product(X21,X22,X23)
=> product(X21,X22,sK5(X21,X22)) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
( ~ product(inverse(sK3),inverse(sK4),sK0)
& product(sK2,sK1,sK4)
& product(inverse(sK1),inverse(sK2),sK3)
& ! [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,sK5(X21,X22)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[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(f16,plain,
! [X6] : product(X6,inverse(X6),sK0),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X5] : product(inverse(X5),X5,sK0),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
product(inverse(sK1),inverse(sK2),sK3),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
product(sK2,sK1,sK4),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
~ product(inverse(sK3),inverse(sK4),sK0),
inference(cnf_transformation,[],[f10]) ).
cnf(c_49,negated_conjecture,
~ product(inverse(sK3),inverse(sK4),sK0),
inference(cnf_transformation,[],[f20]) ).
cnf(c_50,negated_conjecture,
product(sK2,sK1,sK4),
inference(cnf_transformation,[],[f19]) ).
cnf(c_51,negated_conjecture,
product(inverse(sK1),inverse(sK2),sK3),
inference(cnf_transformation,[],[f18]) ).
cnf(c_52,negated_conjecture,
product(inverse(X0),X0,sK0),
inference(cnf_transformation,[],[f17]) ).
cnf(c_53,negated_conjecture,
product(X0,inverse(X0),sK0),
inference(cnf_transformation,[],[f16]) ).
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_315,plain,
( ~ product(inverse(X0),X1,X2)
| ~ product(X1,X3,X0)
| product(X2,X3,sK0) ),
inference(superposition,[status(thm)],[c_52,c_56]) ).
cnf(c_317,plain,
( ~ product(X0,X1,X2)
| ~ product(sK0,X0,X3)
| product(X3,X1,X2) ),
inference(superposition,[status(thm)],[c_54,c_56]) ).
cnf(c_318,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,sK0)
| product(X2,X3,X0) ),
inference(superposition,[status(thm)],[c_55,c_56]) ).
cnf(c_508,plain,
( ~ product(X0,X1,X2)
| ~ product(sK0,X1,X3)
| product(inverse(X0),X2,X3) ),
inference(superposition,[status(thm)],[c_52,c_57]) ).
cnf(c_1011,plain,
( ~ product(inverse(sK2),X0,sK1)
| product(sK3,X0,sK0) ),
inference(superposition,[status(thm)],[c_51,c_315]) ).
cnf(c_1373,plain,
( ~ product(sK0,X0,X1)
| product(X1,inverse(X0),sK0) ),
inference(superposition,[status(thm)],[c_53,c_317]) ).
cnf(c_1623,plain,
( ~ product(X0,X1,sK0)
| product(sK0,X1,inverse(X0)) ),
inference(superposition,[status(thm)],[c_52,c_318]) ).
cnf(c_2080,plain,
( ~ product(sK0,sK1,X0)
| product(inverse(sK2),sK4,X0) ),
inference(superposition,[status(thm)],[c_50,c_508]) ).
cnf(c_3120,plain,
~ product(sK0,sK4,inverse(sK3)),
inference(superposition,[status(thm)],[c_1373,c_49]) ).
cnf(c_3703,plain,
~ product(sK3,sK4,sK0),
inference(superposition,[status(thm)],[c_1623,c_3120]) ).
cnf(c_4574,plain,
( ~ product(sK0,sK1,sK1)
| product(sK3,sK4,sK0) ),
inference(superposition,[status(thm)],[c_2080,c_1011]) ).
cnf(c_4579,plain,
~ product(sK0,sK1,sK1),
inference(global_subsumption_just,[status(thm)],[c_4574,c_3703,c_4574]) ).
cnf(c_4731,plain,
$false,
inference(superposition,[status(thm)],[c_54,c_4579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n003.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 : Fri May 3 00:10:05 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.69/1.15 % SZS status Started for theBenchmark.p
% 3.69/1.15 % SZS status Theorem for theBenchmark.p
% 3.69/1.15
% 3.69/1.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.69/1.15
% 3.69/1.15 ------ iProver source info
% 3.69/1.15
% 3.69/1.15 git: date: 2024-05-02 19:28:25 +0000
% 3.69/1.15 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.69/1.15 git: non_committed_changes: false
% 3.69/1.15
% 3.69/1.15 ------ Parsing...
% 3.69/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.69/1.15
% 3.69/1.15 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 3.69/1.15
% 3.69/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.69/1.15 ------ Proving...
% 3.69/1.15 ------ Problem Properties
% 3.69/1.15
% 3.69/1.15
% 3.69/1.15 clauses 10
% 3.69/1.15 conjectures 10
% 3.69/1.15 EPR 5
% 3.69/1.15 Horn 10
% 3.69/1.15 unary 8
% 3.69/1.15 binary 0
% 3.69/1.15 lits 16
% 3.69/1.15 lits eq 0
% 3.69/1.15 fd_pure 0
% 3.69/1.15 fd_pseudo 0
% 3.69/1.15 fd_cond 0
% 3.69/1.15 fd_pseudo_cond 0
% 3.69/1.15 AC symbols 0
% 3.69/1.15
% 3.69/1.15 ------ Input Options Time Limit: Unbounded
% 3.69/1.15
% 3.69/1.15
% 3.69/1.15 ------
% 3.69/1.15 Current options:
% 3.69/1.15 ------
% 3.69/1.15
% 3.69/1.15
% 3.69/1.15
% 3.69/1.15
% 3.69/1.15 ------ Proving...
% 3.69/1.15
% 3.69/1.15
% 3.69/1.15 % SZS status Theorem for theBenchmark.p
% 3.69/1.15
% 3.69/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.15
% 3.69/1.16
%------------------------------------------------------------------------------