%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG378-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 12:54:08 PM UTC 2026
% Result : Unsatisfiable 31.39s 8.85s
% Output : CNFRefutation 31.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 25 unt; 0 def)
% Number of atoms : 115 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 111 ( 56 ~; 55 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 109 ( 0 sgn 109 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
fof(f79,axiom,
! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(X3,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f97,axiom,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f100,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f126,axiom,
! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f528,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_RealVector_Odist__class_Odist(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X3,X1,X0),c_RealVector_Odist__class_Odist(X3,X2,X0),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dist__triangle3_0) ).
fof(f543,axiom,
! [X0,X1] : c_RealVector_Odist__class_Odist(X0,X1,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dist__real__def_0) ).
fof(f574,axiom,
! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f623,negated_conjecture,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f624,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_b,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f626,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f647,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f664,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
fof(f672,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f673,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
tcf(c_675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X0,X3,X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X1,X3,X2)
| ~ c_HOL_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_691,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X0,X3,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_RealVector_Odist__class_Odist(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X3,X1,X0),c_RealVector_Odist__class_Odist(X3,X2,X0),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
inference(cnf_transformation,[],[f528]) ).
tcf(c_1048,plain,
! [X0: $i,X1: $i] : c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Odist__class_Odist(X0,X1,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f543]) ).
tcf(c_1078,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f574]) ).
tcf(c_1122,negated_conjecture,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f623]) ).
tcf(c_1123,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_b,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f624]) ).
tcf(c_1125,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f626]) ).
tcf(c_1146,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f647]) ).
tcf(c_1163,plain,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f664]) ).
tcf(c_1171,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f672]) ).
tcf(c_1172,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f673]) ).
tcf(c_1532,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_1078]) ).
tcf(c_1700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_RealVector_Odist__class_Odist(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X3,X1,X0),c_RealVector_Odist__class_Odist(X3,X2,X0),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
inference(prop_impl_just,[status(thm)],[c_1034]) ).
tcf(c_5577,plain,
c_lessequals(c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_1122,c_1048]) ).
tcf(c_6498,plain,
~ c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_1123,c_1048]) ).
tcf(c_8711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_RealVector_Odist__class_Odist(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X3,X1,X0),c_RealVector_Odist__class_Odist(X3,X2,X0),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1700,c_1163]) ).
tcf(c_8712,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(c_RealVector_Odist__class_Odist(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X2,X0,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_8711]) ).
tcf(c_8809,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1532,c_1146]) ).
tcf(c_8810,plain,
! [X0: $i,X1: $i] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_8809]) ).
tcf(c_8877,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_691,c_1172]) ).
tcf(c_8878,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_8877]) ).
tcf(c_8893,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_694,c_1172]) ).
tcf(c_8894,plain,
! [X0: $i,X1: $i] :
( ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_8893]) ).
tcf(c_9227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_718,c_1125]) ).
tcf(c_9228,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X0,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_9227]) ).
tcf(c_9268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_675,c_1171]) ).
tcf(c_9269,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_9268]) ).
tcf(c_11308,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X1,X0,tc_RealDef_Oreal) ),
inference(prop_impl_just,[status(thm)],[c_8878]) ).
tcf(c_11309,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(renaming,[status(thm)],[c_11308]) ).
tcf(c_12068,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(bin_hyper_res,[status(thm)],[c_9269,c_11309]) ).
tcf(c_13600,plain,
~ c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_c,c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_6498,c_8810]) ).
tcf(c_17253,plain,
! [X0: $i,X1: $i] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal) ),
inference(prop_impl_just,[status(thm)],[c_8894]) ).
tcf(c_17254,plain,
! [X0: $i,X1: $i] :
( ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(renaming,[status(thm)],[c_17253]) ).
tcf(c_17483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X2,tc_RealDef_Oreal) ),
inference(prop_impl_just,[status(thm)],[c_9228]) ).
tcf(c_17484,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_HOL_Oord__class_Oless(X0,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(renaming,[status(thm)],[c_17483]) ).
tcf(c_25004,plain,
! [X0: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_c,c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_c,c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(instantiation,[status(thm)],[c_12068]) ).
tcf(c_26917,plain,
! [X0: $i] :
( c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_c,c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_c,c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X0,v_b,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X0,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X0,v_b,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X0,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(instantiation,[status(thm)],[c_25004]) ).
tcf(c_26918,plain,
! [X0: $i] : c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X0,v_b,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X0,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(instantiation,[status(thm)],[c_8712]) ).
tcf(c_28533,plain,
~ c_HOL_Oord__class_Oless(v_c,c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_17254,c_5577]) ).
tcf(c_40135,plain,
c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(instantiation,[status(thm)],[c_26918]) ).
tcf(c_46401,plain,
( c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_c,c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_c,c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Odist__class_Odist(v_b,v_m,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(instantiation,[status(thm)],[c_26917]) ).
tcf(c_46402,plain,
( c_HOL_Oord__class_Oless(v_c,c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_c,c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(instantiation,[status(thm)],[c_17484]) ).
tcf(c_46403,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_46402,c_46401,c_40135,c_28533,c_13600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG378-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.36 % Computer : n018.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Fri Sep 25 05:32:50 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.40 Running first-order theorem proving
% 0.07/0.40 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
% 0.07/0.42
% 0.07/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.42
% 0.07/0.42 % Detected problem language: tptp
% 0.07/0.43 % Proving...
% 31.39/8.85 % SZS status Started for theBenchmark.p
% 31.39/8.85 % SZS status Unsatisfiable for theBenchmark.p
% 31.39/8.85
% 31.39/8.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.39/8.85
% 31.39/8.85 % ------ iProver source info
% 31.39/8.85
% 31.39/8.85 % git: date: 2026-07-19 20:42:38 +0200
% 31.39/8.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.39/8.85 % git: non_committed_changes: false
% 31.39/8.85
% 31.39/8.85 % ------ Parsing...% successful
% 31.39/8.85
% 31.39/8.85
% 31.39/8.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.39/8.85
% 31.39/8.85 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e sup_sim: 53 sf_s rm: 52 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 52 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 52 0s sf_e pe_s pe_e %
% 31.39/8.85
% 31.39/8.85 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.39/8.85
% 31.39/8.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.39/8.85 % ------ Proving...
% 31.39/8.85 % ------ Problem Properties
% 31.39/8.85
% 31.39/8.85 %
% 31.39/8.85 % clauses 295
% 31.39/8.85 % conjectures 0
% 31.39/8.85 % EPR 10
% 31.39/8.85 % Horn 255
% 31.39/8.85 % unary 102
% 31.39/8.85 % binary 109
% 31.39/8.85 % lits 586
% 31.39/8.85 % lits eq 159
% 31.39/8.85 % fd_pure 0
% 31.39/8.85 % fd_pseudo 0
% 31.39/8.85 % fd_cond 21
% 31.39/8.85 % fd_pseudo_cond 20
% 31.39/8.85 % AC symbols 0
% 31.39/8.85
% 31.39/8.85 % ------ Input Options Time Limit: Unbounded
% 31.39/8.85
% 31.39/8.85
% 31.39/8.85 % ------
% 31.39/8.85 % Current options:
% 31.39/8.85 % ------
% 31.39/8.85
% 31.39/8.85
% 31.39/8.85 %
% 31.39/8.85
% 31.39/8.85 % ------ Proving...
% 31.39/8.85 %
% 31.39/8.85
% 31.39/8.85 % SZS status Unsatisfiable for theBenchmark.p
% 31.39/8.85
% 31.39/8.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.39/8.85
% 31.39/8.85
%------------------------------------------------------------------------------