%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG353-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 18:03:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.54s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 13 unt; 0 nHn; 15 RR)
% Number of literals : 21 ( 0 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(553,axiom,
equal(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Complex_OIm(c_Complex_Oii)),
file('ALG353-1.p',unknown),
[] ).
cnf(556,axiom,
equal(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(u,v,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Odist__class_Odist(u,v,tc_Complex_Ocomplex)),
file('ALG353-1.p',unknown),
[] ).
cnf(620,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('ALG353-1.p',unknown),
[] ).
cnf(742,axiom,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('ALG353-1.p',unknown),
[] ).
cnf(743,axiom,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('ALG353-1.p',unknown),
[] ).
cnf(744,axiom,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('ALG353-1.p',unknown),
[] ).
cnf(745,axiom,
c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('ALG353-1.p',unknown),
[] ).
cnf(761,plain,
c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[553,745]),
[iquote('0:Rew:553.0,745.0')] ).
cnf(762,plain,
c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[553,744]),
[iquote('0:Rew:553.0,744.0')] ).
cnf(774,plain,
c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[553,743]),
[iquote('0:Rew:553.0,743.0')] ).
cnf(775,plain,
c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[553,742]),
[iquote('0:Rew:553.0,742.0')] ).
cnf(776,plain,
c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Odist__class_Odist(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[556,774]),
[iquote('0:Rew:556.0,774.0')] ).
cnf(777,plain,
c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Odist__class_Odist(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[556,761]),
[iquote('0:Rew:556.0,761.0')] ).
cnf(838,plain,
( ~ c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Odist__class_Odist(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_Complex_Oii,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Odist__class_Odist(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_Complex_OIm(c_Complex_Oii),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[553,620,556]),
[iquote('0:Rew:553.0,620.3,553.0,620.2,556.0,620.2,553.0,620.1,553.0,620.0,556.0,620.0')] ).
cnf(839,plain,
$false,
inference(mrr,[status(thm)],[838,777,762,776,775]),
[iquote('0:MRR:838.0,838.1,838.2,838.3,777.0,762.0,776.0,775.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ALG353-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 06:00:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.54
% 0.19/0.54 SPASS V 3.9
% 0.19/0.54 SPASS beiseite: Proof found.
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.54 SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 662 clauses.
% 0.19/0.54 SPASS allocated 76764 KBytes.
% 0.19/0.54 SPASS spent 0:00:00.20 on the problem.
% 0.19/0.54 0:00:00.06 for the input.
% 0.19/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.54 0:00:00.00 for inferences.
% 0.19/0.54 0:00:00.00 for the backtracking.
% 0.19/0.54 0:00:00.09 for the reduction.
% 0.19/0.54
% 0.19/0.54
% 0.19/0.54 Here is a proof with depth 0, length 15 :
% 0.19/0.54 % SZS output start Refutation
% See solution above
% 0.19/0.54 Formulae used in the proof : cls_complex__Im__i_0 cls_dist__complex__def_0 cls_CHAINED_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.19/0.54
%------------------------------------------------------------------------------