%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG072+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 18:02:13 EDT 2022
% Result : Theorem 7.05s 7.24s
% Output : Refutation 7.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of clauses : 52 ( 18 unt; 0 nHn; 52 RR)
% Number of literals : 118 ( 0 equ; 70 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
sorti1(unit1),
file('ALG072+1.p',unknown),
[] ).
cnf(4,axiom,
sorti2(unit2),
file('ALG072+1.p',unknown),
[] ).
cnf(5,axiom,
sorti1(skc1),
file('ALG072+1.p',unknown),
[] ).
cnf(6,axiom,
sorti2(skf3(u)),
file('ALG072+1.p',unknown),
[] ).
cnf(7,axiom,
sorti2(skf2(u)),
file('ALG072+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ sorti1(u)
| sorti2(h(u)) ),
file('ALG072+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sorti2(u)
| sorti1(j(u)) ),
file('ALG072+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti2(u)
| equal(h(j(u)),u) ),
file('ALG072+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sorti1(u)
| equal(j(h(u)),u) ),
file('ALG072+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ sorti1(u)
| equal(op1(u,unit1),u) ),
file('ALG072+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ sorti2(u)
| equal(op2(unit2,u),u) ),
file('ALG072+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ sorti2(u)
| equal(op2(skf2(u),skf3(u)),u) ),
file('ALG072+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ sorti2(u)
| ~ equal(op2(skf2(u),u),skf3(u))
| equal(u,unit2) ),
file('ALG072+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op2(h(v),h(u)),h(op1(v,u))) ),
file('ALG072+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(u)),j(op2(v,u))) ),
file('ALG072+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| ~ equal(skc1,unit1)
| ~ equal(op1(v,u),skc1) ),
file('ALG072+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| ~ equal(op1(v,u),skc1)
| equal(op1(v,skc1),u) ),
file('ALG072+1.p',unknown),
[] ).
cnf(24,plain,
sorti1(j(unit2)),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.0')] ).
cnf(27,plain,
sorti2(h(skc1)),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.0')] ).
cnf(28,plain,
sorti2(h(unit1)),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.0')] ).
cnf(29,plain,
equal(j(h(skc1)),skc1),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.0,11.0')] ).
cnf(30,plain,
equal(j(h(unit1)),unit1),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.0')] ).
cnf(34,plain,
( ~ sorti2(u)
| equal(op1(j(unit2),j(u)),j(op2(unit2,u))) ),
inference(res,[status(thm),theory(equality)],[4,21]),
[iquote('0:Res:4.0,21.0')] ).
cnf(42,plain,
( ~ sorti1(u)
| equal(op2(h(u),h(skc1)),h(op1(u,skc1))) ),
inference(res,[status(thm),theory(equality)],[5,20]),
[iquote('0:Res:5.0,20.1')] ).
cnf(44,plain,
( ~ sorti2(u)
| equal(op1(j(unit2),j(u)),j(u)) ),
inference(rew,[status(thm),theory(equality)],[14,34]),
[iquote('0:Rew:14.1,34.1')] ).
cnf(104,plain,
( ~ sorti2(h(unit1))
| equal(op1(j(unit2),unit1),unit1) ),
inference(spr,[status(thm),theory(equality)],[30,44]),
[iquote('0:SpR:30.0,44.1')] ).
cnf(107,plain,
equal(op1(j(unit2),unit1),unit1),
inference(ssi,[status(thm)],[104,28]),
[iquote('0:SSi:104.0,28.0')] ).
cnf(111,plain,
( ~ sorti1(j(unit2))
| equal(j(unit2),unit1) ),
inference(spr,[status(thm),theory(equality)],[107,13]),
[iquote('0:SpR:107.0,13.1')] ).
cnf(113,plain,
equal(j(unit2),unit1),
inference(ssi,[status(thm)],[111,24]),
[iquote('0:SSi:111.0,24.0')] ).
cnf(117,plain,
equal(op1(unit1,unit1),unit1),
inference(rew,[status(thm),theory(equality)],[113,107]),
[iquote('0:Rew:113.0,107.0')] ).
cnf(141,plain,
( ~ sorti1(unit1)
| ~ sorti1(unit1)
| ~ equal(skc1,unit1)
| ~ equal(skc1,unit1) ),
inference(spl,[status(thm),theory(equality)],[117,22]),
[iquote('0:SpL:117.0,22.3')] ).
cnf(143,plain,
( ~ sorti1(unit1)
| ~ equal(skc1,unit1) ),
inference(obv,[status(thm),theory(equality)],[141]),
[iquote('0:Obv:141.2')] ).
cnf(144,plain,
~ equal(skc1,unit1),
inference(ssi,[status(thm)],[143,2]),
[iquote('0:SSi:143.0,2.0')] ).
cnf(286,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(u))
| ~ sorti1(j(v))
| ~ equal(j(op2(v,u)),skc1)
| equal(op1(j(v),skc1),j(u)) ),
inference(spl,[status(thm),theory(equality)],[21,23]),
[iquote('0:SpL:21.2,23.2')] ).
cnf(297,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ equal(j(op2(v,u)),skc1)
| equal(op1(j(v),skc1),j(u)) ),
inference(ssi,[status(thm)],[286,9]),
[iquote('0:SSi:286.3,286.2,9.1,9.1')] ).
cnf(371,plain,
( ~ sorti2(u)
| ~ sorti1(j(u))
| equal(h(op1(j(u),skc1)),op2(u,h(skc1))) ),
inference(spr,[status(thm),theory(equality)],[10,42]),
[iquote('0:SpR:10.1,42.1')] ).
cnf(377,plain,
( ~ sorti2(u)
| equal(h(op1(j(u),skc1)),op2(u,h(skc1))) ),
inference(ssi,[status(thm)],[371,9]),
[iquote('0:SSi:371.1,9.1')] ).
cnf(758,plain,
( ~ sorti2(u)
| ~ sorti2(skf3(u))
| ~ sorti2(skf2(u))
| ~ equal(j(u),skc1)
| equal(op1(j(skf2(u)),skc1),j(skf3(u))) ),
inference(spl,[status(thm),theory(equality)],[18,297]),
[iquote('0:SpL:18.1,297.2')] ).
cnf(777,plain,
( ~ sorti2(u)
| ~ equal(j(u),skc1)
| equal(op1(j(skf2(u)),skc1),j(skf3(u))) ),
inference(ssi,[status(thm)],[758,7,6]),
[iquote('0:SSi:758.2,758.1,7.0,6.0')] ).
cnf(1811,plain,
( ~ sorti2(u)
| ~ sorti2(skf2(u))
| ~ equal(j(u),skc1)
| equal(op2(skf2(u),h(skc1)),h(j(skf3(u)))) ),
inference(spr,[status(thm),theory(equality)],[777,377]),
[iquote('0:SpR:777.2,377.1')] ).
cnf(1824,plain,
( ~ sorti2(u)
| ~ equal(j(u),skc1)
| equal(op2(skf2(u),h(skc1)),h(j(skf3(u)))) ),
inference(ssi,[status(thm)],[1811,7]),
[iquote('0:SSi:1811.1,7.0')] ).
cnf(14467,plain,
( ~ sorti2(h(skc1))
| ~ sorti2(h(skc1))
| ~ equal(j(h(skc1)),skc1)
| ~ equal(h(j(skf3(h(skc1)))),skf3(h(skc1)))
| equal(h(skc1),unit2) ),
inference(spl,[status(thm),theory(equality)],[1824,19]),
[iquote('0:SpL:1824.2,19.1')] ).
cnf(14485,plain,
( ~ sorti2(h(skc1))
| ~ equal(j(h(skc1)),skc1)
| ~ equal(h(j(skf3(h(skc1)))),skf3(h(skc1)))
| equal(h(skc1),unit2) ),
inference(obv,[status(thm),theory(equality)],[14467]),
[iquote('0:Obv:14467.0')] ).
cnf(14486,plain,
( ~ sorti2(h(skc1))
| ~ equal(skc1,skc1)
| ~ equal(h(j(skf3(h(skc1)))),skf3(h(skc1)))
| equal(h(skc1),unit2) ),
inference(rew,[status(thm),theory(equality)],[29,14485]),
[iquote('0:Rew:29.0,14485.1')] ).
cnf(14487,plain,
( ~ sorti2(h(skc1))
| ~ equal(h(j(skf3(h(skc1)))),skf3(h(skc1)))
| equal(h(skc1),unit2) ),
inference(obv,[status(thm),theory(equality)],[14486]),
[iquote('0:Obv:14486.1')] ).
cnf(14488,plain,
( ~ equal(h(j(skf3(h(skc1)))),skf3(h(skc1)))
| equal(h(skc1),unit2) ),
inference(ssi,[status(thm)],[14487,27]),
[iquote('0:SSi:14487.0,27.0')] ).
cnf(14498,plain,
( ~ sorti2(skf3(h(skc1)))
| ~ equal(skf3(h(skc1)),skf3(h(skc1)))
| equal(h(skc1),unit2) ),
inference(spl,[status(thm),theory(equality)],[10,14488]),
[iquote('0:SpL:10.1,14488.0')] ).
cnf(14499,plain,
( ~ sorti2(skf3(h(skc1)))
| equal(h(skc1),unit2) ),
inference(obv,[status(thm),theory(equality)],[14498]),
[iquote('0:Obv:14498.1')] ).
cnf(14500,plain,
equal(h(skc1),unit2),
inference(ssi,[status(thm)],[14499,6,27]),
[iquote('0:SSi:14499.0,6.0,27.0')] ).
cnf(14502,plain,
equal(j(unit2),skc1),
inference(rew,[status(thm),theory(equality)],[14500,29]),
[iquote('0:Rew:14500.0,29.0')] ).
cnf(14674,plain,
equal(skc1,unit1),
inference(rew,[status(thm),theory(equality)],[113,14502]),
[iquote('0:Rew:113.0,14502.0')] ).
cnf(14675,plain,
$false,
inference(mrr,[status(thm)],[14674,144]),
[iquote('0:MRR:14674.0,144.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG072+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 00:18:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 7.05/7.24
% 7.05/7.24 SPASS V 3.9
% 7.05/7.24 SPASS beiseite: Proof found.
% 7.05/7.24 % SZS status Theorem
% 7.05/7.24 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.05/7.24 SPASS derived 9416 clauses, backtracked 0 clauses, performed 0 splits and kept 1875 clauses.
% 7.05/7.24 SPASS allocated 118406 KBytes.
% 7.05/7.24 SPASS spent 0:00:05.43 on the problem.
% 7.05/7.24 0:00:00.04 for the input.
% 7.05/7.24 0:00:00.03 for the FLOTTER CNF translation.
% 7.05/7.24 0:00:00.16 for inferences.
% 7.05/7.24 0:00:00.00 for the backtracking.
% 7.05/7.24 0:00:05.16 for the reduction.
% 7.05/7.24
% 7.05/7.24
% 7.05/7.24 Here is a proof with depth 5, length 52 :
% 7.05/7.24 % SZS output start Refutation
% See solution above
% 7.05/7.24 Formulae used in the proof : ax2 ax4 ax7 ax8 ax3 co1
% 7.05/7.24
%------------------------------------------------------------------------------