%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV154+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:16:33 PM UTC 2026
% Result : Theorem 0.30s 1.07s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 98 ( 37 equ)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 109 ( 25 ~; 16 |; 58 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 17 ( 0 sgn 14 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [X1] :
( ( leq(X1,pred(pv10))
& leq(n0,X1) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 )
& ! [X0] :
( ( leq(X0,pred(pv12))
& leq(n0,X0) )
=> a_select3(q,pv10,X0) = 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)))))) )
& 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)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0004) ).
fof(f54,negated_conjecture,
~ ( ( ! [X1] :
( ( leq(X1,pred(pv10))
& leq(n0,X1) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 )
& ! [X0] :
( ( leq(X0,pred(pv12))
& leq(n0,X0) )
=> a_select3(q,pv10,X0) = 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)))))) )
& 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(negated_conjecture,[status(cth)],[f53]) ).
fof(f143,plain,
( ! [X1] :
( ~ leq(X1,pred(pv10))
| ~ leq(n0,X1)
| sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 )
& ! [X0] :
( ~ leq(X0,pred(pv12))
| ~ leq(n0,X0)
| a_select3(q,pv10,X0) = 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)))))) )
& 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(ennf_transformation,[],[f54]) ).
fof(f144,plain,
( ! [X1] :
( ~ leq(X1,pred(pv10))
| ~ leq(n0,X1)
| sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 )
& ! [X0] :
( ~ leq(X0,pred(pv12))
| ~ leq(n0,X0)
| a_select3(q,pv10,X0) = 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)))))) )
& 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(flattening,[],[f143]) ).
fof(f197,plain,
( ! [X2] :
( ~ leq(X2,pred(pv10))
| ~ leq(n0,X2)
| n1 = sum(n0,n4,a_select3(q,X2,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)))))
& ? [X0] :
( leq(X0,pv12)
& leq(n0,X0)
& pv12 = X0
& 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)))))) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) ) ),
inference(rectify,[],[f144]) ).
fof(f198,plain,
( ! [X2] :
( ~ leq(X2,pred(pv10))
| ~ leq(n0,X2)
| n1 = sum(n0,n4,a_select3(q,X2,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)))))
& leq(sK31,pv12)
& leq(n0,sK31)
& pv12 = sK31
& 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(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X0,sK31)],[f197]) ).
fof(f315,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,[],[f198]) ).
fof(f318,plain,
pv12 = sK31,
inference(cnf_transformation,[],[f198]) ).
fof(f319,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,[],[f198]) ).
fof(f380,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,[],[f319,f318,f318]) ).
tcf(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,[],[f380]) ).
tcf(c_160,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,[],[f315]) ).
tcf(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_160]) ).
tcf(c_2463,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV154+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 18:33:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 0.30/1.07 % SZS status Started for theBenchmark.p
% 0.30/1.07 % SZS status Theorem for theBenchmark.p
% 0.30/1.07
% 0.30/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.30/1.07
% 0.30/1.07 % ------ iProver source info
% 0.30/1.07
% 0.30/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.30/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.30/1.07 % git: non_committed_changes: false
% 0.30/1.07
% 0.30/1.07 % ------ Parsing...
% 0.30/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.30/1.07
% 0.30/1.07 % ------ Preprocessing...%
% 0.30/1.07
% 0.30/1.07 % SZS status Theorem for theBenchmark.p
% 0.30/1.07
% 0.30/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.30/1.07
% 0.30/1.07
%------------------------------------------------------------------------------