%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV153+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 4.47s 6.30s
% Output : CNFRefutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 152 ( 51 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 169 ( 55 ~; 42 |; 60 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn 41 !; 3 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( X0 != X1
& leq(X0,X1) )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
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
=> a_select3(q,pv10,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)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0003) ).
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
=> a_select3(q,pv10,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)))))) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,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
& a_select3(q,pv10,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)))))) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,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
& a_select3(q,pv10,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)))))) ) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f99,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(flattening,[],[f98]) ).
fof(f118,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
& 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)))))) ) ),
inference(rectify,[],[f95]) ).
fof(f119,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(sK0,pv12)
& leq(n0,sK0)
& pv12 != sK0
& a_select3(q,pv10,sK0) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,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,[sK0]),skolemize(X0,sK0)],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ( ~ leq(X0,pred(X1))
| gt(X1,X0) )
& ( ~ gt(X1,X0)
| leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f124,plain,
! [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)))))) ),
inference(cnf_transformation,[],[f119]) ).
fof(f129,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,[],[f119]) ).
fof(f130,plain,
leq(sK0,pv12),
inference(cnf_transformation,[],[f119]) ).
fof(f131,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f119]) ).
fof(f132,plain,
pv12 != sK0,
inference(cnf_transformation,[],[f119]) ).
fof(f133,plain,
a_select3(q,pv10,sK0) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,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,[],[f119]) ).
fof(f135,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f140,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f170,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
! [X1] :
( ~ leq(X1,minus(pv12,n1))
| ~ 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)))))) ),
inference(definition_unfolding,[],[f124,f170]) ).
fof(f209,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f140,f170]) ).
tcf(c_49,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,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,sK0),
inference(cnf_transformation,[],[f133]) ).
tcf(c_50,negated_conjecture,
sK0 != pv12,
inference(cnf_transformation,[],[f132]) ).
tcf(c_51,negated_conjecture,
leq(n0,sK0),
inference(cnf_transformation,[],[f131]) ).
tcf(c_52,negated_conjecture,
leq(sK0,pv12),
inference(cnf_transformation,[],[f130]) ).
tcf(c_53,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,[],[f129]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( ( 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)))))) = a_select3(q,pv10,X0) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv12,n1)) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| ( X0 = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( leq(X1,minus(X0,n1))
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_694,plain,
divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),pv70) != a_select3(q,pv10,sK0),
inference(light_normalisation,[status(thm)],[c_49,c_53]) ).
tcf(c_695,plain,
! [X0: $i] :
( ( divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),pv70) = a_select3(q,pv10,X0) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv12,n1)) ),
inference(light_normalisation,[status(thm)],[c_58,c_53]) ).
tcf(c_1820,plain,
! [X0: $i] :
( ( divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),pv70) = a_select3(q,pv10,X0) )
| ~ gt(pv12,X0)
| ~ leq(n0,X0) ),
inference(superposition,[status(thm)],[c_65,c_695]) ).
tcf(c_2208,plain,
( ( divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),pv70) = a_select3(q,pv10,sK0) )
| ~ gt(pv12,sK0) ),
inference(superposition,[status(thm)],[c_51,c_1820]) ).
tcf(c_2233,plain,
~ gt(pv12,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_2208,c_694]) ).
tcf(c_2477,plain,
( gt(pv12,sK0)
| ( sK0 = pv12 )
| ~ leq(sK0,pv12) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2478,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2477,c_2233,c_50,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV153+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n004.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 18:37:57 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.43 % Proving...
% 4.47/6.30 % SZS status Started for theBenchmark.p
% 4.47/6.30 % SZS status Theorem for theBenchmark.p
% 4.47/6.30
% 4.47/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.47/6.30
% 4.47/6.30 % ------ iProver source info
% 4.47/6.30
% 4.47/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.47/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.47/6.30 % git: non_committed_changes: false
% 4.47/6.30
% 4.47/6.30 % ------ Parsing...
% 4.47/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.47/6.30
% 4.47/6.30 % ------ Preprocessing... sup_sim: 12 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.47/6.30
% 4.47/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.47/6.30
% 4.47/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.47/6.30 % ------ Proving...
% 4.47/6.30 % ------ Problem Properties
% 4.47/6.30
% 4.47/6.30 %
% 4.47/6.30 % clauses 80
% 4.47/6.30 % conjectures 9
% 4.47/6.30 % EPR 48
% 4.47/6.30 % Horn 73
% 4.47/6.30 % unary 58
% 4.47/6.30 % binary 10
% 4.47/6.30 % lits 129
% 4.47/6.30 % lits eq 46
% 4.47/6.30 % fd_pure 0
% 4.47/6.30 % fd_pseudo 0
% 4.47/6.30 % fd_cond 6
% 4.47/6.30 % fd_pseudo_cond 2
% 4.47/6.30 % AC symbols 0
% 4.47/6.30
% 4.47/6.30 % ------ Schedule dynamic 5 is on
% 4.47/6.30
% 4.47/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.47/6.30
% 4.47/6.30
% 4.47/6.30 % ------
% 4.47/6.30 % Current options:
% 4.47/6.30 % ------
% 4.47/6.30
% 4.47/6.30
% 4.47/6.30 %
% 4.47/6.30
% 4.47/6.30 % ------ Proving...
% 4.47/6.30 %
% 4.47/6.30
% 4.47/6.30 % SZS status Theorem for theBenchmark.p
% 4.47/6.30
% 4.47/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.47/6.30
% 4.47/6.30
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