TSTP Solution File: SWV154+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWV154+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.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 22:31:22 EDT 2023
% Result : Theorem 0.49s 1.15s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 121 ( 46 equ)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 133 ( 28 ~; 16 |; 73 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn; 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [X17] :
( ( leq(X17,pred(pv10))
& leq(n0,X17) )
=> n1 = sum(n0,n4,a_select3(q,X17,tptp_sum_index)) )
& ! [X13] :
( ( leq(X13,pred(pv12))
& leq(n0,X13) )
=> a_select3(q,pv10,X13) = divide(sqrt(times(minus(a_select3(center,X13,n0),a_select2(x,pv10)),minus(a_select3(center,X13,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) )
=> ! [X3] :
( ( leq(X3,pv12)
& leq(n0,X3) )
=> ( pv12 = X3
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,X3,n0),a_select2(x,pv10)),minus(a_select3(center,X3,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0004) ).
fof(f54,negated_conjecture,
~ ( ( ! [X17] :
( ( leq(X17,pred(pv10))
& leq(n0,X17) )
=> n1 = sum(n0,n4,a_select3(q,X17,tptp_sum_index)) )
& ! [X13] :
( ( leq(X13,pred(pv12))
& leq(n0,X13) )
=> a_select3(q,pv10,X13) = divide(sqrt(times(minus(a_select3(center,X13,n0),a_select2(x,pv10)),minus(a_select3(center,X13,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) )
=> ! [X3] :
( ( leq(X3,pv12)
& leq(n0,X3) )
=> ( pv12 = X3
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,X3,n0),a_select2(x,pv10)),minus(a_select3(center,X3,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f114,plain,
~ ( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index)) )
& ! [X1] :
( ( leq(X1,pred(pv12))
& leq(n0,X1) )
=> a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) )
=> ! [X2] :
( ( leq(X2,pv12)
& leq(n0,X2) )
=> ( pv12 = X2
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
inference(rectify,[],[f54]) ).
fof(f156,plain,
( ? [X2] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = X2
& leq(X2,pv12)
& leq(n0,X2) )
& ! [X0] :
( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) )
& ! [X1] :
( a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| ~ leq(X1,pred(pv12))
| ~ leq(n0,X1) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) ),
inference(ennf_transformation,[],[f114]) ).
fof(f157,plain,
( ? [X2] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = X2
& leq(X2,pv12)
& leq(n0,X2) )
& ! [X0] :
( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) )
& ! [X1] :
( a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| ~ leq(X1,pred(pv12))
| ~ leq(n0,X1) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) ),
inference(flattening,[],[f156]) ).
fof(f224,plain,
( ? [X0] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = X0
& leq(X0,pv12)
& leq(n0,X0) )
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(X1,pred(pv10))
| ~ leq(n0,X1) )
& ! [X2] :
( divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = a_select3(q,pv10,X2)
| ~ leq(X2,pred(pv12))
| ~ leq(n0,X2) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) ),
inference(rectify,[],[f157]) ).
fof(f225,plain,
( ? [X0] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = X0
& leq(X0,pv12)
& leq(n0,X0) )
=> ( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = sK31
& leq(sK31,pv12)
& leq(n0,sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = sK31
& leq(sK31,pv12)
& leq(n0,sK31)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(X1,pred(pv10))
| ~ leq(n0,X1) )
& ! [X2] :
( divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = a_select3(q,pv10,X2)
| ~ leq(X2,pred(pv12))
| ~ leq(n0,X2) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f224,f225]) ).
fof(f337,plain,
pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))),
inference(cnf_transformation,[],[f226]) ).
fof(f346,plain,
pv12 = sK31,
inference(cnf_transformation,[],[f226]) ).
fof(f347,plain,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(cnf_transformation,[],[f226]) ).
fof(f408,plain,
divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),pv70),
inference(definition_unfolding,[],[f347,f346,f346]) ).
cnf(c_157,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),pv70),
inference(cnf_transformation,[],[f408]) ).
cnf(c_166,negated_conjecture,
sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(cnf_transformation,[],[f337]) ).
cnf(c_2462,plain,
divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),pv70),
inference(light_normalisation,[status(thm)],[c_157,c_166]) ).
cnf(c_2463,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV154+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 07:03:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.49/1.15 % SZS status Started for theBenchmark.p
% 0.49/1.15 % SZS status Theorem for theBenchmark.p
% 0.49/1.15
% 0.49/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.49/1.15
% 0.49/1.15 ------ iProver source info
% 0.49/1.15
% 0.49/1.15 git: date: 2023-05-31 18:12:56 +0000
% 0.49/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.49/1.15 git: non_committed_changes: false
% 0.49/1.15 git: last_make_outside_of_git: false
% 0.49/1.15
% 0.49/1.15 ------ Parsing...
% 0.49/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.49/1.15
% 0.49/1.15 ------ Preprocessing...
% 0.49/1.15
% 0.49/1.15 % SZS status Theorem for theBenchmark.p
% 0.49/1.15
% 0.49/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.49/1.15
% 0.49/1.15
%------------------------------------------------------------------------------