%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG378-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 06:50:06 AM UTC 2026
% Result : Unsatisfiable 83.40s 12.01s
% Output : CNFRefutation 83.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 31 unt; 0 def)
% Number of atoms : 66 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 26 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 77 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
cnf(c_45,plain,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add]) ).
fof(cls_le__add__right__mono_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_lessequals(VAR_1,c_HOL_Oplus__class_Oplus(VAR_2,VAR_4,VAR_0),VAR_0)
| ~ c_lessequals(VAR_4,VAR_3,VAR_0)
| c_lessequals(VAR_1,c_HOL_Oplus__class_Oplus(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(c_48,plain,
( ~ c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,A),A)
| ~ c_lessequals(E,D,A)
| c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[cls_le__add__right__mono_0]) ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(c_174,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]) ).
fof(cls_diff__minus__eq__add_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_HOL_Ominus__class_Ominus(VAR_1,c_HOL_Ouminus__class_Ouminus(VAR_2,VAR_0),VAR_0) = c_HOL_Oplus__class_Oplus(VAR_1,VAR_2,VAR_0)
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_diff__minus__eq__add_0) ).
cnf(c_182,plain,
( c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oplus__class_Oplus(B,C,A)
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_diff__minus__eq__add_0]) ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(c_250,plain,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add]) ).
fof(cls_minus__diff__eq_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(VAR_1,VAR_2,VAR_0),VAR_0) = c_HOL_Ominus__class_Ominus(VAR_2,VAR_1,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(c_258,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_HOL_Ominus__class_Ominus(C,B,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_minus__diff__eq_0]) ).
fof(clsarity_RealDef__Oreal__RealVector_Ometric__space,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
cnf(c_278,plain,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__RealVector_Ometric__space]) ).
fof(cls_dist__triangle3_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_RealVector_Odist__class_Odist(VAR_1,VAR_2,VAR_0),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(VAR_3,VAR_1,VAR_0),c_RealVector_Odist__class_Odist(VAR_3,VAR_2,VAR_0),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(VAR_0) ),
file('theBenchmark.p',cls_dist__triangle3_0) ).
cnf(c_281,plain,
( c_lessequals(c_RealVector_Odist__class_Odist(B,C,A),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(D,B,A),c_RealVector_Odist__class_Odist(D,C,A),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(A) ),
inference(clausify,[status(thm)],[cls_dist__triangle3_0]) ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(c_292,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs]) ).
fof(cls_abs__minus__cancel_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(VAR_1,VAR_0),VAR_0) = c_HOL_Oabs__class_Oabs(VAR_1,VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(VAR_0) ),
file('theBenchmark.p',cls_abs__minus__cancel_0) ).
cnf(c_314,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Oabs__class_Oabs(B,A)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(A) ),
inference(clausify,[status(thm)],[cls_abs__minus__cancel_0]) ).
cnf(c_589,plain,
c_lessequals(c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(C,A,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_278,c_281]) ).
cnf(c_598,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_250,c_258]) ).
cnf(c_599,plain,
c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(copy,[status(thm)],[c_598]) ).
cnf(c_623,plain,
c_HOL_Ominus__class_Ominus(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_174,c_182]) ).
cnf(c_624,plain,
c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(copy,[status(thm)],[c_623]) ).
cnf(c_684,plain,
( ~ c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(D,C,tc_RealDef_Oreal)
| c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_45,c_48]) ).
cnf(c_5449,plain,
( ~ c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(D,C,tc_RealDef_Oreal)
| c_lessequals(A,c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(paramod,[status(thm)],[c_624,c_684]) ).
cnf(c_685,plain,
( ~ c_lessequals(A,c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(D,C,tc_RealDef_Oreal)
| c_lessequals(A,c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(paramod,[status(thm)],[c_624,c_5449]) ).
fof(cls_conjecture_1,axiom,
~ 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('theBenchmark.p',cls_conjecture_1) ).
cnf(c_716,plain,
~ 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(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_717,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_b,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_624,c_716]) ).
fof(cls_conjecture_0,axiom,
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('theBenchmark.p',cls_conjecture_0) ).
cnf(c_718,plain,
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(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_dist__real__def_0,axiom,
! [VAR_0,VAR_1] : c_RealVector_Odist__class_Odist(VAR_0,VAR_1,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(VAR_0,VAR_1,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_dist__real__def_0) ).
cnf(c_730,plain,
c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_dist__real__def_0]) ).
cnf(c_938,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_314,c_292]) ).
cnf(c_5450,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(C,A,tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_730,c_589]) ).
cnf(c_5451,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_730,c_5450]) ).
cnf(c_5452,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_730,c_5451]) ).
cnf(c_1029,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_624,c_5452]) ).
cnf(c_5453,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v_m,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_599,c_717]) ).
cnf(c_1523,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_m,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_938,c_5453]) ).
cnf(c_5454,plain,
( ~ c_lessequals(A,c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(A,c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_685,c_718]) ).
cnf(c_5447,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_5454,c_1029]) ).
cnf(c_5448,plain,
$false,
inference(resolve,[status(thm)],[c_5447,c_1523]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG378-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n013.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 21:55:36 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 3629711 was started by sandbox2 on n013,
% 0.15/0.44 % Sat Sep 26 21:55:36 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 83.40/12.01
% 83.40/12.01 % SZS status Unsatisfiable for theBenchmark
% 83.40/12.01
% 83.40/12.01 % Proof 1 at 2.85 (+ 0.45) seconds.
% 83.40/12.01 % Length of proof is 26.
% 83.40/12.01 % Level of proof is 5.
% 83.40/12.01 % Maximum clause weight is 34.000.
% 83.40/12.01 % Given clauses 253.
% 83.40/12.01
% 83.40/12.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------