TSTP Solution File: ALG210+2 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ALG210+2 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 02:04:17 EDT 2024
% Result : Theorem 0.59s 1.11s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X1] :
( element(X1)
<=> ? [X2] :
( times(X1,X1) = X2
& times(X1,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,conjecture,
! [X0,X1,X2] :
( ( times(X0,X1) = X2
& element(X1)
& element(X0) )
=> element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
fof(f4,negated_conjecture,
~ ! [X0,X1,X2] :
( ( times(X0,X1) = X2
& element(X1)
& element(X0) )
=> element(X2) ),
inference(negated_conjecture,[],[f3]) ).
fof(f5,plain,
! [X0] :
( element(X0)
<=> ? [X1] :
( times(X0,X0) = X1
& times(X0,X1) = X0 ) ),
inference(rectify,[],[f2]) ).
fof(f6,plain,
? [X0,X1,X2] :
( ~ element(X2)
& times(X0,X1) = X2
& element(X1)
& element(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f7,plain,
? [X0,X1,X2] :
( ~ element(X2)
& times(X0,X1) = X2
& element(X1)
& element(X0) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ( element(X0)
| ! [X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0 ) )
& ( ? [X1] :
( times(X0,X0) = X1
& times(X0,X1) = X0 )
| ~ element(X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X0] :
( ( element(X0)
| ! [X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0 ) )
& ( ? [X2] :
( times(X0,X0) = X2
& times(X0,X2) = X0 )
| ~ element(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
! [X0] :
( ? [X2] :
( times(X0,X0) = X2
& times(X0,X2) = X0 )
=> ( times(X0,X0) = sK0(X0)
& times(X0,sK0(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
! [X0] :
( ( element(X0)
| ! [X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0 ) )
& ( ( times(X0,X0) = sK0(X0)
& times(X0,sK0(X0)) = X0 )
| ~ element(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
fof(f12,plain,
( ? [X0,X1,X2] :
( ~ element(X2)
& times(X0,X1) = X2
& element(X1)
& element(X0) )
=> ( ~ element(sK3)
& sK3 = times(sK1,sK2)
& element(sK2)
& element(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
( ~ element(sK3)
& sK3 = times(sK1,sK2)
& element(sK2)
& element(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f7,f12]) ).
fof(f14,plain,
! [X2,X0,X1] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0] :
( times(X0,sK0(X0)) = X0
| ~ element(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
! [X0] :
( times(X0,X0) = sK0(X0)
| ~ element(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1] :
( element(X0)
| times(X0,X0) != X1
| times(X0,X1) != X0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
element(sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
element(sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
sK3 = times(sK1,sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
~ element(sK3),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0] :
( element(X0)
| times(X0,times(X0,X0)) != X0 ),
inference(equality_resolution,[],[f17]) ).
cnf(c_49,plain,
times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[],[f14]) ).
cnf(c_50,plain,
( times(X0,times(X0,X0)) != X0
| element(X0) ),
inference(cnf_transformation,[],[f22]) ).
cnf(c_51,plain,
( ~ element(X0)
| times(X0,X0) = sK0(X0) ),
inference(cnf_transformation,[],[f16]) ).
cnf(c_52,plain,
( ~ element(X0)
| times(X0,sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f15]) ).
cnf(c_53,negated_conjecture,
~ element(sK3),
inference(cnf_transformation,[],[f21]) ).
cnf(c_54,negated_conjecture,
times(sK1,sK2) = sK3,
inference(cnf_transformation,[],[f20]) ).
cnf(c_55,negated_conjecture,
element(sK2),
inference(cnf_transformation,[],[f19]) ).
cnf(c_56,negated_conjecture,
element(sK1),
inference(cnf_transformation,[],[f18]) ).
cnf(c_159,plain,
times(sK1,sK2) = sP0_iProver_def,
definition ).
cnf(c_160,negated_conjecture,
element(sK1),
inference(demodulation,[status(thm)],[c_56]) ).
cnf(c_161,negated_conjecture,
element(sK2),
inference(demodulation,[status(thm)],[c_55]) ).
cnf(c_162,negated_conjecture,
sP0_iProver_def = sK3,
inference(demodulation,[status(thm)],[c_54,c_159]) ).
cnf(c_164,plain,
X0 = X0,
theory(equality) ).
cnf(c_166,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_168,plain,
( X0 != X1
| ~ element(X1)
| element(X0) ),
theory(equality) ).
cnf(c_265,plain,
times(sK2,sK2) = sK0(sK2),
inference(superposition,[status(thm)],[c_161,c_51]) ).
cnf(c_266,plain,
times(sK1,sK1) = sK0(sK1),
inference(superposition,[status(thm)],[c_160,c_51]) ).
cnf(c_268,plain,
times(sK2,times(X0,sK1)) = times(sP0_iProver_def,X0),
inference(superposition,[status(thm)],[c_159,c_49]) ).
cnf(c_269,plain,
times(sK1,times(X0,sK1)) = times(sK0(sK1),X0),
inference(superposition,[status(thm)],[c_266,c_49]) ).
cnf(c_270,plain,
times(sK2,times(X0,sK2)) = times(sK0(sK2),X0),
inference(superposition,[status(thm)],[c_265,c_49]) ).
cnf(c_271,plain,
times(times(X0,times(X1,X2)),X3) = times(X1,times(X3,times(X2,X0))),
inference(superposition,[status(thm)],[c_49,c_49]) ).
cnf(c_280,plain,
times(sK2,sK0(sK2)) = sK2,
inference(superposition,[status(thm)],[c_161,c_52]) ).
cnf(c_281,plain,
times(sK1,sK0(sK1)) = sK1,
inference(superposition,[status(thm)],[c_160,c_52]) ).
cnf(c_298,plain,
times(sK0(sK1),times(X0,sK1)) = times(sK1,X0),
inference(superposition,[status(thm)],[c_281,c_49]) ).
cnf(c_300,plain,
times(sK2,times(X0,times(sK1,X1))) = times(sP0_iProver_def,times(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_268]) ).
cnf(c_301,plain,
times(sK2,sK0(sK1)) = times(sP0_iProver_def,sK1),
inference(superposition,[status(thm)],[c_266,c_268]) ).
cnf(c_305,plain,
( sK3 != X0
| ~ element(X0)
| element(sK3) ),
inference(instantiation,[status(thm)],[c_168]) ).
cnf(c_311,plain,
times(sK0(sK1),sK1) = times(sK1,sK0(sK1)),
inference(superposition,[status(thm)],[c_266,c_269]) ).
cnf(c_314,plain,
times(sK0(sK1),sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_311,c_281]) ).
cnf(c_318,plain,
( X0 != X1
| sK3 != X1
| sK3 = X0 ),
inference(instantiation,[status(thm)],[c_166]) ).
cnf(c_321,plain,
( X0 != sK3
| sK3 != sK3
| sK3 = X0 ),
inference(instantiation,[status(thm)],[c_318]) ).
cnf(c_322,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_164]) ).
cnf(c_325,plain,
times(sK1,times(X0,sK0(sK1))) = times(sK1,X0),
inference(superposition,[status(thm)],[c_314,c_49]) ).
cnf(c_327,plain,
times(sP0_iProver_def,sK0(sK1)) = times(sK2,sK1),
inference(superposition,[status(thm)],[c_314,c_268]) ).
cnf(c_337,plain,
( sK3 != sK3
| sP0_iProver_def != sK3
| sK3 = sP0_iProver_def ),
inference(instantiation,[status(thm)],[c_321]) ).
cnf(c_344,plain,
times(sK0(sK2),sK2) = times(sK2,sK0(sK2)),
inference(superposition,[status(thm)],[c_265,c_270]) ).
cnf(c_347,plain,
times(sK0(sK2),sK2) = sK2,
inference(light_normalisation,[status(thm)],[c_344,c_280]) ).
cnf(c_351,plain,
( sK3 != sP0_iProver_def
| ~ element(sP0_iProver_def)
| element(sK3) ),
inference(instantiation,[status(thm)],[c_305]) ).
cnf(c_373,plain,
( times(sP0_iProver_def,times(sP0_iProver_def,sP0_iProver_def)) != sP0_iProver_def
| element(sP0_iProver_def) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_407,plain,
times(X0,times(X1,times(X2,X3))) = times(X2,times(X3,times(X0,X1))),
inference(demodulation,[status(thm)],[c_271,c_49]) ).
cnf(c_446,plain,
times(sK1,times(sK0(sK1),times(X0,X1))) = times(X0,times(X1,sK1)),
inference(superposition,[status(thm)],[c_281,c_407]) ).
cnf(c_635,plain,
times(X0,times(sK1,sK1)) = times(sK1,times(sK1,X0)),
inference(superposition,[status(thm)],[c_298,c_446]) ).
cnf(c_667,plain,
times(sK1,times(sK1,X0)) = times(X0,sK0(sK1)),
inference(light_normalisation,[status(thm)],[c_635,c_266]) ).
cnf(c_786,plain,
times(X0,times(X1,times(sK1,sK1))) = times(times(X0,X1),sK0(sK1)),
inference(superposition,[status(thm)],[c_667,c_407]) ).
cnf(c_799,plain,
times(times(X0,X1),sK0(sK1)) = times(X0,times(X1,sK0(sK1))),
inference(light_normalisation,[status(thm)],[c_786,c_266]) ).
cnf(c_845,plain,
times(X0,times(sK0(sK1),X1)) = times(X1,times(X0,sK0(sK1))),
inference(demodulation,[status(thm)],[c_799,c_49]) ).
cnf(c_882,plain,
times(sK2,times(sK2,sK0(sK1))) = times(sK0(sK2),sK0(sK1)),
inference(superposition,[status(thm)],[c_845,c_270]) ).
cnf(c_899,plain,
times(X0,times(sK0(sK1),sK1)) = times(sK1,X0),
inference(superposition,[status(thm)],[c_845,c_325]) ).
cnf(c_902,plain,
times(X0,sK1) = times(sK1,X0),
inference(light_normalisation,[status(thm)],[c_899,c_314]) ).
cnf(c_908,plain,
times(sK0(sK2),sK0(sK1)) = times(sK2,times(sP0_iProver_def,sK1)),
inference(light_normalisation,[status(thm)],[c_882,c_301]) ).
cnf(c_932,plain,
times(sP0_iProver_def,sK0(sK1)) = times(sK1,sK2),
inference(demodulation,[status(thm)],[c_327,c_902]) ).
cnf(c_937,plain,
times(sP0_iProver_def,sK0(sK1)) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_932,c_159]) ).
cnf(c_1266,plain,
times(sK1,times(X0,times(sK2,X1))) = times(sP0_iProver_def,times(X0,X1)),
inference(demodulation,[status(thm)],[c_300,c_407]) ).
cnf(c_1274,plain,
times(sK1,times(sK0(sK2),sK2)) = times(sP0_iProver_def,times(sK2,sK2)),
inference(superposition,[status(thm)],[c_270,c_1266]) ).
cnf(c_1281,plain,
times(sK1,times(X0,sK0(sK2))) = times(sP0_iProver_def,times(X0,sK2)),
inference(superposition,[status(thm)],[c_265,c_1266]) ).
cnf(c_1305,plain,
times(sP0_iProver_def,sK0(sK2)) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_1274,c_265,c_159,c_347]) ).
cnf(c_1631,plain,
times(sK0(sK2),times(X0,sP0_iProver_def)) = times(sP0_iProver_def,X0),
inference(superposition,[status(thm)],[c_1305,c_49]) ).
cnf(c_1768,plain,
times(sK0(sK2),sK0(sK1)) = times(sP0_iProver_def,times(sK1,sK2)),
inference(superposition,[status(thm)],[c_1281,c_667]) ).
cnf(c_1773,plain,
times(sK0(sK2),sK0(sK1)) = times(sP0_iProver_def,sP0_iProver_def),
inference(light_normalisation,[status(thm)],[c_1768,c_159,c_908]) ).
cnf(c_2339,plain,
times(sP0_iProver_def,times(sK0(sK2),sK0(sK1))) = times(sP0_iProver_def,sK0(sK1)),
inference(superposition,[status(thm)],[c_1631,c_845]) ).
cnf(c_2345,plain,
times(sP0_iProver_def,times(sP0_iProver_def,sP0_iProver_def)) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_2339,c_937,c_1773]) ).
cnf(c_2350,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2345,c_373,c_351,c_337,c_322,c_162,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : ALG210+2 : TPTP v8.1.2. Released v3.1.0.
% 0.10/0.11 % Command : run_iprover %s %d THM
% 0.10/0.32 % Computer : n022.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu May 2 22:46:12 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 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
% 0.59/1.11 % SZS status Started for theBenchmark.p
% 0.59/1.11 % SZS status Theorem for theBenchmark.p
% 0.59/1.11
% 0.59/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.59/1.11
% 0.59/1.11 ------ iProver source info
% 0.59/1.11
% 0.59/1.11 git: date: 2024-05-02 19:28:25 +0000
% 0.59/1.11 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.59/1.11 git: non_committed_changes: false
% 0.59/1.11
% 0.59/1.11 ------ Parsing...
% 0.59/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.59/1.11
% 0.59/1.11 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.59/1.11
% 0.59/1.11 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.59/1.11
% 0.59/1.11 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.59/1.11 ------ Proving...
% 0.59/1.11 ------ Problem Properties
% 0.59/1.11
% 0.59/1.11
% 0.59/1.11 clauses 9
% 0.59/1.11 conjectures 4
% 0.59/1.11 EPR 4
% 0.59/1.11 Horn 9
% 0.59/1.11 unary 6
% 0.59/1.11 binary 3
% 0.59/1.11 lits 12
% 0.59/1.11 lits eq 6
% 0.59/1.11 fd_pure 0
% 0.59/1.11 fd_pseudo 0
% 0.59/1.11 fd_cond 0
% 0.59/1.11 fd_pseudo_cond 0
% 0.59/1.11 AC symbols 0
% 0.59/1.11
% 0.59/1.11 ------ Schedule dynamic 5 is on
% 0.59/1.11
% 0.59/1.11 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.59/1.11
% 0.59/1.11
% 0.59/1.11 ------
% 0.59/1.11 Current options:
% 0.59/1.11 ------
% 0.59/1.11
% 0.59/1.11
% 0.59/1.11
% 0.59/1.11
% 0.59/1.11 ------ Proving...
% 0.59/1.11
% 0.59/1.11
% 0.59/1.11 % SZS status Theorem for theBenchmark.p
% 0.59/1.11
% 0.59/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.59/1.11
% 0.59/1.12
%------------------------------------------------------------------------------