TSTP Solution File: GRP194+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 00:58:38 EDT 2023
% Result : Theorem 1.02s 1.19s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 18 unt; 0 def)
% Number of atoms : 173 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 179 ( 74 ~; 70 |; 24 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn; 50 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X1] :
( group_member(X1,f)
=> group_member(phi(X1),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f4,axiom,
! [X1,X2] :
( ( group_member(X2,f)
& group_member(X1,f) )
=> multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f5,axiom,
! [X1] :
( group_member(X1,h)
=> ? [X2] :
( phi(X2) = X1
& group_member(X2,f) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f6,axiom,
! [X0,X1] :
( left_zero(X0,X1)
<=> ( ! [X2] :
( group_member(X2,X0)
=> multiply(X0,X1,X2) = X1 )
& group_member(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero) ).
fof(f7,axiom,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero_for_f) ).
fof(f8,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_zero_h) ).
fof(f9,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(negated_conjecture,[],[f8]) ).
fof(f10,plain,
! [X0] :
( group_member(X0,f)
=> group_member(phi(X0),h) ),
inference(rectify,[],[f3]) ).
fof(f11,plain,
! [X0,X1] :
( ( group_member(X1,f)
& group_member(X0,f) )
=> multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1)) ),
inference(rectify,[],[f4]) ).
fof(f12,plain,
! [X0] :
( group_member(X0,h)
=> ? [X1] :
( phi(X1) = X0
& group_member(X1,f) ) ),
inference(rectify,[],[f5]) ).
fof(f13,plain,
~ left_zero(h,phi(f_left_zero)),
inference(flattening,[],[f9]) ).
fof(f18,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f11]) ).
fof(f20,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0] :
( ? [X1] :
( phi(X1) = X0
& group_member(X1,f) )
| ~ group_member(X0,h) ),
inference(ennf_transformation,[],[f12]) ).
fof(f22,plain,
! [X0,X1] :
( left_zero(X0,X1)
<=> ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0] :
( ? [X1] :
( phi(X1) = X0
& group_member(X1,f) )
=> ( phi(sK0(X0)) = X0
& group_member(sK0(X0),f) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0] :
( ( phi(sK0(X0)) = X0
& group_member(sK0(X0),f) )
| ~ group_member(X0,h) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) )
| ~ left_zero(X0,X1) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) )
| ~ left_zero(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X3] :
( multiply(X0,X1,X3) = X1
| ~ group_member(X3,X0) )
& group_member(X1,X0) )
| ~ left_zero(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
=> ( multiply(X0,X1,sK1(X0,X1)) != X1
& group_member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ( multiply(X0,X1,sK1(X0,X1)) != X1
& group_member(sK1(X0,X1),X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X3] :
( multiply(X0,X1,X3) = X1
| ~ group_member(X3,X0) )
& group_member(X1,X0) )
| ~ left_zero(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28]) ).
fof(f32,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0] :
( group_member(sK0(X0),f)
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X0] :
( phi(sK0(X0)) = X0
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
! [X0,X1] :
( group_member(X1,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f37,plain,
! [X3,X0,X1] :
( multiply(X0,X1,X3) = X1
| ~ group_member(X3,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f38,plain,
! [X0,X1] :
( left_zero(X0,X1)
| group_member(sK1(X0,X1),X0)
| ~ group_member(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f39,plain,
! [X0,X1] :
( left_zero(X0,X1)
| multiply(X0,X1,sK1(X0,X1)) != X1
| ~ group_member(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[],[f7]) ).
fof(f41,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[],[f13]) ).
cnf(c_51,plain,
( ~ group_member(X0,f)
| group_member(phi(X0),h) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_52,plain,
( ~ group_member(X0,f)
| ~ group_member(X1,f)
| multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1)) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_53,plain,
( ~ group_member(X0,h)
| phi(sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_54,plain,
( ~ group_member(X0,h)
| group_member(sK0(X0),f) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_55,plain,
( multiply(X0,X1,sK1(X0,X1)) != X1
| ~ group_member(X1,X0)
| left_zero(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_56,plain,
( ~ group_member(X0,X1)
| group_member(sK1(X1,X0),X1)
| left_zero(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_57,plain,
( ~ group_member(X0,X1)
| ~ left_zero(X1,X2)
| multiply(X1,X2,X0) = X2 ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_58,plain,
( ~ left_zero(X0,X1)
| group_member(X1,X0) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_59,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[],[f40]) ).
cnf(c_60,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[],[f41]) ).
cnf(c_207,plain,
( X0 != f
| X1 != f_left_zero
| group_member(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_58,c_59]) ).
cnf(c_208,plain,
group_member(f_left_zero,f),
inference(unflattening,[status(thm)],[c_207]) ).
cnf(c_212,plain,
( multiply(X0,X1,sK1(X0,X1)) != X1
| phi(f_left_zero) != X1
| X0 != h
| ~ group_member(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_55,c_60]) ).
cnf(c_213,plain,
( multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))) != phi(f_left_zero)
| ~ group_member(phi(f_left_zero),h) ),
inference(unflattening,[status(thm)],[c_212]) ).
cnf(c_235,plain,
( phi(f_left_zero) != X0
| X1 != h
| ~ group_member(X0,X1)
| group_member(sK1(X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_56,c_60]) ).
cnf(c_236,plain,
( ~ group_member(phi(f_left_zero),h)
| group_member(sK1(h,phi(f_left_zero)),h) ),
inference(unflattening,[status(thm)],[c_235]) ).
cnf(c_479,plain,
group_member(f_left_zero,f),
inference(superposition,[status(thm)],[c_59,c_58]) ).
cnf(c_492,plain,
( ~ group_member(X0,f)
| phi(sK0(phi(X0))) = phi(X0) ),
inference(superposition,[status(thm)],[c_51,c_53]) ).
cnf(c_502,plain,
( ~ group_member(X0,h)
| phi(sK0(sK1(h,X0))) = sK1(h,X0)
| left_zero(h,X0) ),
inference(superposition,[status(thm)],[c_56,c_53]) ).
cnf(c_515,plain,
( ~ group_member(X0,f)
| multiply(h,phi(f_left_zero),phi(X0)) = phi(multiply(f,f_left_zero,X0)) ),
inference(superposition,[status(thm)],[c_479,c_52]) ).
cnf(c_553,plain,
( ~ group_member(X0,h)
| ~ left_zero(f,X1)
| multiply(f,X1,sK0(X0)) = X1 ),
inference(superposition,[status(thm)],[c_54,c_57]) ).
cnf(c_635,plain,
phi(sK0(phi(f_left_zero))) = phi(f_left_zero),
inference(superposition,[status(thm)],[c_479,c_492]) ).
cnf(c_658,plain,
( ~ group_member(f_left_zero,f)
| group_member(phi(f_left_zero),h) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_662,plain,
( ~ group_member(sK0(phi(f_left_zero)),f)
| group_member(phi(f_left_zero),h) ),
inference(superposition,[status(thm)],[c_635,c_51]) ).
cnf(c_665,plain,
group_member(phi(f_left_zero),h),
inference(global_subsumption_just,[status(thm)],[c_662,c_208,c_658]) ).
cnf(c_802,plain,
( phi(sK0(sK1(h,phi(f_left_zero)))) = sK1(h,phi(f_left_zero))
| left_zero(h,phi(f_left_zero)) ),
inference(superposition,[status(thm)],[c_665,c_502]) ).
cnf(c_803,plain,
phi(sK0(sK1(h,phi(f_left_zero)))) = sK1(h,phi(f_left_zero)),
inference(forward_subsumption_resolution,[status(thm)],[c_802,c_60]) ).
cnf(c_851,plain,
( ~ group_member(X0,h)
| multiply(h,phi(f_left_zero),phi(sK0(X0))) = phi(multiply(f,f_left_zero,sK0(X0))) ),
inference(superposition,[status(thm)],[c_54,c_515]) ).
cnf(c_968,plain,
( ~ group_member(sK0(sK1(h,phi(f_left_zero))),f)
| group_member(sK1(h,phi(f_left_zero)),h) ),
inference(superposition,[status(thm)],[c_803,c_51]) ).
cnf(c_971,plain,
group_member(sK1(h,phi(f_left_zero)),h),
inference(global_subsumption_just,[status(thm)],[c_968,c_208,c_236,c_658]) ).
cnf(c_978,plain,
( ~ left_zero(f,X0)
| multiply(f,X0,sK0(sK1(h,phi(f_left_zero)))) = X0 ),
inference(superposition,[status(thm)],[c_971,c_553]) ).
cnf(c_1032,plain,
multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero)))) = f_left_zero,
inference(superposition,[status(thm)],[c_59,c_978]) ).
cnf(c_1366,plain,
multiply(h,phi(f_left_zero),phi(sK0(sK1(h,phi(f_left_zero))))) = phi(multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero))))),
inference(superposition,[status(thm)],[c_971,c_851]) ).
cnf(c_1369,plain,
multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))) = phi(f_left_zero),
inference(light_normalisation,[status(thm)],[c_1366,c_803,c_1032]) ).
cnf(c_1380,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1369,c_658,c_213,c_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 21:04:19 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.02/1.19 % SZS status Started for theBenchmark.p
% 1.02/1.19 % SZS status Theorem for theBenchmark.p
% 1.02/1.19
% 1.02/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.02/1.19
% 1.02/1.19 ------ iProver source info
% 1.02/1.19
% 1.02/1.19 git: date: 2023-05-31 18:12:56 +0000
% 1.02/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.02/1.19 git: non_committed_changes: false
% 1.02/1.19 git: last_make_outside_of_git: false
% 1.02/1.19
% 1.02/1.19 ------ Parsing...
% 1.02/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.02/1.19
% 1.02/1.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 1.02/1.19
% 1.02/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.02/1.19
% 1.02/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.02/1.19 ------ Proving...
% 1.02/1.19 ------ Problem Properties
% 1.02/1.19
% 1.02/1.19
% 1.02/1.19 clauses 12
% 1.02/1.19 conjectures 1
% 1.02/1.19 EPR 2
% 1.02/1.19 Horn 11
% 1.02/1.19 unary 2
% 1.02/1.19 binary 4
% 1.02/1.19 lits 29
% 1.02/1.19 lits eq 5
% 1.02/1.19 fd_pure 0
% 1.02/1.19 fd_pseudo 0
% 1.02/1.19 fd_cond 0
% 1.02/1.19 fd_pseudo_cond 0
% 1.02/1.19 AC symbols 0
% 1.02/1.19
% 1.02/1.19 ------ Schedule dynamic 5 is on
% 1.02/1.19
% 1.02/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.02/1.19
% 1.02/1.19
% 1.02/1.19 ------
% 1.02/1.19 Current options:
% 1.02/1.19 ------
% 1.02/1.19
% 1.02/1.19
% 1.02/1.19
% 1.02/1.19
% 1.02/1.19 ------ Proving...
% 1.02/1.19
% 1.02/1.19
% 1.02/1.19 % SZS status Theorem for theBenchmark.p
% 1.02/1.19
% 1.02/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.02/1.19
% 1.02/1.19
%------------------------------------------------------------------------------