%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV163+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 03:16:34 PM UTC 2026
% Result : Theorem 1.12s 1.29s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 139 ( 28 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 142 ( 50 ~; 52 |; 31 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 7 ( 1 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 : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 68 ( 0 sgn 65 !; 3 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',totality) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',transitivity_gt) ).
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).
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(f53,conjecture,
( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X1] :
( ( leq(X1,tptp_minus_1)
& 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)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0013) ).
fof(f54,negated_conjecture,
~ ( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X1] :
( ( leq(X1,tptp_minus_1)
& 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(negated_conjecture,[status(cth)],[f53]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f103,plain,
! [X0,X1,X2] :
( ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(flattening,[],[f105]) ).
fof(f108,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(flattening,[],[f108]) ).
fof(f143,plain,
( ! [X0] :
( ~ leq(X0,pred(pv10))
| ~ leq(n0,X0)
| sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10)
& ? [X1] :
( leq(X1,tptp_minus_1)
& 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(ennf_transformation,[],[f54]) ).
fof(f144,plain,
( ! [X0] :
( ~ leq(X0,pred(pv10))
| ~ leq(n0,X0)
| sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10)
& ? [X1] :
( leq(X1,tptp_minus_1)
& 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(flattening,[],[f143]) ).
fof(f197,plain,
( ! [X1] :
( ~ leq(X1,pred(pv10))
| ~ leq(n0,X1)
| n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index)) )
& leq(pv10,n135299)
& leq(n0,pv10)
& ? [X0] :
( leq(X0,tptp_minus_1)
& 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)))))) ) ),
inference(rectify,[],[f144]) ).
fof(f198,plain,
( ! [X1] :
( ~ leq(X1,pred(pv10))
| ~ leq(n0,X1)
| n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index)) )
& leq(pv10,n135299)
& leq(n0,pv10)
& leq(sK31,tptp_minus_1)
& leq(n0,sK31)
& a_select3(q,pv10,sK31) != 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(f199,plain,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f201,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f205,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f312,plain,
leq(sK31,tptp_minus_1),
inference(cnf_transformation,[],[f198]) ).
fof(f313,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f321,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| gt(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_51,plain,
! [X0: $i] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f201]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| ( X0 = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_158,negated_conjecture,
leq(n0,sK31),
inference(cnf_transformation,[],[f313]) ).
tcf(c_159,negated_conjecture,
leq(sK31,tptp_minus_1),
inference(cnf_transformation,[],[f312]) ).
tcf(c_169,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f321]) ).
tcf(c_203,plain,
~ gt(n0,n0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_234,plain,
( gt(n0,n0)
| ( n0 = n0 ) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_5857,negated_conjecture,
leq(sK31,tptp_minus_1),
inference(demodulation,[status(thm)],[c_159]) ).
tcf(c_5858,negated_conjecture,
leq(n0,sK31),
inference(demodulation,[status(thm)],[c_158]) ).
tcf(c_5863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( gt(X0,X2)
| ~ gt(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_10420,plain,
! [X0: $i] :
( gt(n0,X0)
| ~ gt(tptp_minus_1,X0) ),
inference(superposition,[status(thm)],[c_169,c_50]) ).
tcf(c_10529,plain,
( gt(n0,n0)
| ~ gt(tptp_minus_1,n0) ),
inference(instantiation,[status(thm)],[c_10420]) ).
tcf(c_10880,plain,
! [X0: $i] :
( leq(n0,X0)
| ~ leq(sK31,X0) ),
inference(superposition,[status(thm)],[c_5858,c_53]) ).
tcf(c_11110,plain,
! [X0: $i,X1: $i] :
( gt(X0,X1)
| ~ gt(n0,tptp_minus_1)
| ( X1 != tptp_minus_1 )
| ( X0 != n0 ) ),
inference(instantiation,[status(thm)],[c_5863]) ).
tcf(c_11111,plain,
( gt(n0,n0)
| ~ gt(n0,tptp_minus_1)
| ( n0 != tptp_minus_1 )
| ( n0 != n0 ) ),
inference(instantiation,[status(thm)],[c_11110]) ).
tcf(c_11565,plain,
leq(n0,tptp_minus_1),
inference(superposition,[status(thm)],[c_5857,c_10880]) ).
tcf(c_11594,plain,
( gt(tptp_minus_1,n0)
| ( n0 = tptp_minus_1 ) ),
inference(superposition,[status(thm)],[c_11565,c_55]) ).
tcf(c_11603,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11594,c_11111,c_10529,c_234,c_203,c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV163+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 18:39:21 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.12/1.29 % SZS status Started for theBenchmark.p
% 1.12/1.29 % SZS status Theorem for theBenchmark.p
% 1.12/1.29
% 1.12/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.12/1.29
% 1.12/1.29 % ------ iProver source info
% 1.12/1.29
% 1.12/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.12/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.12/1.29 % git: non_committed_changes: false
% 1.12/1.29
% 1.12/1.29 % ------ Parsing...
% 1.12/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.12/1.29
% 1.12/1.29 % ------ Preprocessing... sup_sim: 15 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.12/1.29
% 1.12/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.12/1.29
% 1.12/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.12/1.29 % ------ Proving...
% 1.12/1.29 % ------ Problem Properties
% 1.12/1.29
% 1.12/1.29 %
% 1.12/1.29 % clauses 166
% 1.12/1.29 % conjectures 6
% 1.12/1.29 % EPR 48
% 1.12/1.29 % Horn 116
% 1.12/1.29 % unary 71
% 1.12/1.29 % binary 34
% 1.12/1.29 % lits 507
% 1.12/1.29 % lits eq 128
% 1.12/1.29 % fd_pure 0
% 1.12/1.29 % fd_pseudo 0
% 1.12/1.29 % fd_cond 6
% 1.12/1.29 % fd_pseudo_cond 4
% 1.12/1.29 % AC symbols 0
% 1.12/1.29
% 1.12/1.29 % ------ Schedule dynamic 5 is on
% 1.12/1.29
% 1.12/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.12/1.29
% 1.12/1.29
% 1.12/1.29 % ------
% 1.12/1.29 % Current options:
% 1.12/1.29 % ------
% 1.12/1.29
% 1.12/1.29
% 1.12/1.29 %
% 1.12/1.29
% 1.12/1.29 % ------ Proving...
% 1.12/1.29 %
% 1.12/1.29
% 1.12/1.29 % SZS status Theorem for theBenchmark.p
% 1.12/1.29
% 1.12/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.12/1.29
% 1.12/1.29
%------------------------------------------------------------------------------