TSTP Solution File: SWV164+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWV164+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 03:13:39 EDT 2024
% Result : Theorem 0.45s 1.13s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 122 ( 18 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 124 ( 43 ~; 31 |; 38 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 16 con; 0-3 aty)
% Number of variables : 55 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f53,conjecture,
( ( ! [X13] :
( ( leq(X13,pred(pv10))
& leq(n0,X13) )
=> n1 = sum(n0,n4,a_select3(q,X13,tptp_sum_index)) )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X17] :
( ( leq(X17,tptp_minus_1)
& leq(n0,X17) )
=> a_select3(q,pv10,X17) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X17)),minus(a_select2(x,pv10),a_select2(mu,X17))),tptp_minus_2),times(a_select2(sigma,X17),a_select2(sigma,X17)))),a_select2(rho,X17)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X17))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0014) ).
fof(f54,negated_conjecture,
~ ( ( ! [X13] :
( ( leq(X13,pred(pv10))
& leq(n0,X13) )
=> n1 = sum(n0,n4,a_select3(q,X13,tptp_sum_index)) )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X17] :
( ( leq(X17,tptp_minus_1)
& leq(n0,X17) )
=> a_select3(q,pv10,X17) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X17)),minus(a_select2(x,pv10),a_select2(mu,X17))),tptp_minus_2),times(a_select2(sigma,X17),a_select2(sigma,X17)))),a_select2(rho,X17)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X17))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f122,plain,
~ ( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index)) )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X1] :
( ( leq(X1,tptp_minus_1)
& leq(n0,X1) )
=> a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
inference(rectify,[],[f54]) ).
fof(f126,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f127,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(flattening,[],[f126]) ).
fof(f164,plain,
( ? [X1] :
( a_select3(q,pv10,X1) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& leq(X1,tptp_minus_1)
& leq(n0,X1) )
& ! [X0] :
( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(ennf_transformation,[],[f122]) ).
fof(f165,plain,
( ? [X1] :
( a_select3(q,pv10,X1) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& leq(X1,tptp_minus_1)
& leq(n0,X1) )
& ! [X0] :
( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(flattening,[],[f164]) ).
fof(f185,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f232,plain,
( ? [X0] :
( a_select3(q,pv10,X0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& leq(X0,tptp_minus_1)
& leq(n0,X0) )
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(X1,pred(pv10))
| ~ leq(n0,X1) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(rectify,[],[f165]) ).
fof(f233,plain,
( ? [X0] :
( a_select3(q,pv10,X0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& leq(X0,tptp_minus_1)
& leq(n0,X0) )
=> ( a_select3(q,pv10,sK31) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& leq(sK31,tptp_minus_1)
& leq(n0,sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f234,plain,
( a_select3(q,pv10,sK31) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& leq(sK31,tptp_minus_1)
& leq(n0,sK31)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(X1,pred(pv10))
| ~ leq(n0,X1) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f232,f233]) ).
fof(f237,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f239,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f242,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f185]) ).
fof(f243,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f325,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f348,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f234]) ).
fof(f349,plain,
leq(sK31,tptp_minus_1),
inference(cnf_transformation,[],[f234]) ).
fof(f357,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
fof(f398,plain,
! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ),
inference(definition_unfolding,[],[f243,f325]) ).
fof(f399,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f242,f325]) ).
cnf(c_51,plain,
~ gt(X0,X0),
inference(cnf_transformation,[],[f237]) ).
cnf(c_53,plain,
( ~ leq(X0,X1)
| ~ leq(X1,X2)
| leq(X0,X2) ),
inference(cnf_transformation,[],[f239]) ).
cnf(c_56,plain,
( ~ gt(X0,X1)
| leq(X1,minus(X0,n1)) ),
inference(cnf_transformation,[],[f398]) ).
cnf(c_57,plain,
( ~ leq(X0,minus(X1,n1))
| gt(X1,X0) ),
inference(cnf_transformation,[],[f399]) ).
cnf(c_158,negated_conjecture,
leq(sK31,tptp_minus_1),
inference(cnf_transformation,[],[f349]) ).
cnf(c_159,negated_conjecture,
leq(n0,sK31),
inference(cnf_transformation,[],[f348]) ).
cnf(c_169,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f357]) ).
cnf(c_211,plain,
~ gt(n0,n0),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_239,plain,
( ~ leq(n0,minus(n0,n1))
| gt(n0,n0) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_8952,plain,
( ~ gt(X0,X1)
| ~ leq(X2,X1)
| leq(X2,minus(X0,n1)) ),
inference(superposition,[status(thm)],[c_56,c_53]) ).
cnf(c_8953,plain,
( ~ leq(X0,sK31)
| leq(X0,tptp_minus_1) ),
inference(superposition,[status(thm)],[c_158,c_53]) ).
cnf(c_8958,plain,
( ~ leq(n0,sK31)
| leq(n0,tptp_minus_1) ),
inference(instantiation,[status(thm)],[c_8953]) ).
cnf(c_9119,plain,
( ~ leq(X0,tptp_minus_1)
| leq(X0,minus(n0,n1)) ),
inference(superposition,[status(thm)],[c_169,c_8952]) ).
cnf(c_9165,plain,
( ~ leq(n0,tptp_minus_1)
| leq(n0,minus(n0,n1)) ),
inference(instantiation,[status(thm)],[c_9119]) ).
cnf(c_9166,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9165,c_8958,c_239,c_211,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV164+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.10/0.12 % Command : run_iprover %s %d THM
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri May 3 00:57:35 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 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
% 0.45/1.13 % SZS status Started for theBenchmark.p
% 0.45/1.13 % SZS status Theorem for theBenchmark.p
% 0.45/1.13
% 0.45/1.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.13
% 0.45/1.13 ------ iProver source info
% 0.45/1.13
% 0.45/1.13 git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.13 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.13 git: non_committed_changes: false
% 0.45/1.13
% 0.45/1.13 ------ Parsing...
% 0.45/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.45/1.13
% 0.45/1.13 ------ Preprocessing... sup_sim: 17 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.45/1.13
% 0.45/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.45/1.13
% 0.45/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.13 ------ Proving...
% 0.45/1.13 ------ Problem Properties
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13 clauses 161
% 0.45/1.13 conjectures 6
% 0.45/1.13 EPR 55
% 0.45/1.13 Horn 111
% 0.45/1.13 unary 66
% 0.45/1.13 binary 34
% 0.45/1.13 lits 502
% 0.45/1.13 lits eq 115
% 0.45/1.13 fd_pure 0
% 0.45/1.13 fd_pseudo 0
% 0.45/1.13 fd_cond 6
% 0.45/1.13 fd_pseudo_cond 4
% 0.45/1.13 AC symbols 0
% 0.45/1.13
% 0.45/1.13 ------ Input Options Time Limit: Unbounded
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13 ------
% 0.45/1.13 Current options:
% 0.45/1.13 ------
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13 ------ Proving...
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13 % SZS status Theorem for theBenchmark.p
% 0.45/1.13
% 0.45/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.13
% 0.45/1.14
%------------------------------------------------------------------------------