TSTP Solution File: GRP715-11 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP715-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Sat Jul 16 11:49:08 EDT 2022
% Result : Unsatisfiable 2.44s 2.60s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 56 RR)
% Number of literals : 56 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(mult(mult(mult(u,v),w),v),mult(u,mult(mult(v,w),v))),
file('GRP715-11.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
file('GRP715-11.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(u,unit),u),
file('GRP715-11.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(unit,u),u),
file('GRP715-11.p',unknown),
[] ).
cnf(10,axiom,
equal(mult(op_a,op_b),unit),
file('GRP715-11.p',unknown),
[] ).
cnf(11,axiom,
equal(mult(op_b,op_a),unit),
file('GRP715-11.p',unknown),
[] ).
cnf(12,axiom,
~ equal(mult(mult(x0__dfg,op_b),op_a),x0__dfg),
file('GRP715-11.p',unknown),
[] ).
cnf(36,plain,
equal(mult(op_b,mult(op_a,op_a)),mult(unit,op_a)),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.0,7.0')] ).
cnf(37,plain,
equal(mult(op_a,mult(op_b,op_b)),mult(unit,op_b)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(41,plain,
equal(mult(op_b,mult(op_a,op_a)),op_a),
inference(rew,[status(thm),theory(equality)],[9,36]),
[iquote('0:Rew:9.0,36.0')] ).
cnf(42,plain,
equal(mult(op_a,mult(op_b,op_b)),op_b),
inference(rew,[status(thm),theory(equality)],[9,37]),
[iquote('0:Rew:9.0,37.0')] ).
cnf(44,plain,
equal(mult(op_b,mult(mult(op_a,op_a),mult(op_a,op_a))),mult(op_a,mult(op_a,op_a))),
inference(spr,[status(thm),theory(equality)],[41,7]),
[iquote('0:SpR:41.0,7.0')] ).
cnf(157,plain,
equal(mult(mult(u,mult(mult(v,w),v)),v),mult(mult(mult(u,v),w),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(160,plain,
equal(mult(u,mult(mult(v,v),v)),mult(mult(u,v),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(162,plain,
equal(mult(mult(u,mult(mult(v,w),v)),w),mult(mult(u,v),mult(mult(w,v),w))),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(163,plain,
equal(mult(op_b,mult(mult(op_a,u),op_a)),mult(mult(unit,u),op_a)),
inference(spr,[status(thm),theory(equality)],[11,6]),
[iquote('0:SpR:11.0,6.0')] ).
cnf(164,plain,
equal(mult(op_a,mult(mult(op_b,u),op_b)),mult(mult(unit,u),op_b)),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(168,plain,
equal(mult(mult(mult(u,mult(v,v)),w),v),mult(mult(u,v),mult(mult(v,w),v))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(175,plain,
equal(mult(op_b,mult(mult(op_a,u),op_a)),mult(u,op_a)),
inference(rew,[status(thm),theory(equality)],[9,163]),
[iquote('0:Rew:9.0,163.0')] ).
cnf(176,plain,
equal(mult(op_a,mult(mult(op_b,u),op_b)),mult(u,op_b)),
inference(rew,[status(thm),theory(equality)],[9,164]),
[iquote('0:Rew:9.0,164.0')] ).
cnf(179,plain,
equal(mult(mult(u,v),mult(v,v)),mult(u,mult(v,mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[7,160]),
[iquote('0:Rew:7.0,160.0')] ).
cnf(181,plain,
equal(mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_a,mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[179,44]),
[iquote('0:Rew:179.0,44.0')] ).
cnf(374,plain,
equal(mult(op_b,mult(op_a,mult(op_a,op_a))),mult(op_a,op_a)),
inference(spr,[status(thm),theory(equality)],[7,175]),
[iquote('0:SpR:7.0,175.0')] ).
cnf(488,plain,
equal(mult(mult(op_a,op_a),op_b),mult(op_a,mult(op_a,op_b))),
inference(spr,[status(thm),theory(equality)],[41,176]),
[iquote('0:SpR:41.0,176.0')] ).
cnf(493,plain,
equal(mult(mult(op_a,op_a),op_b),op_a),
inference(rew,[status(thm),theory(equality)],[8,488,10]),
[iquote('0:Rew:8.0,488.0,10.0,488.0')] ).
cnf(508,plain,
equal(mult(mult(op_a,mult(op_a,op_a)),op_b),mult(op_a,mult(mult(op_a,op_a),op_b))),
inference(spr,[status(thm),theory(equality)],[374,176]),
[iquote('0:SpR:374.0,176.0')] ).
cnf(512,plain,
equal(mult(mult(op_a,mult(op_a,op_a)),op_b),mult(op_a,op_a)),
inference(rew,[status(thm),theory(equality)],[493,508]),
[iquote('0:Rew:493.0,508.0')] ).
cnf(861,plain,
equal(mult(mult(op_a,mult(op_a,op_a)),mult(op_b,op_b)),mult(mult(op_a,op_a),op_b)),
inference(spr,[status(thm),theory(equality)],[512,7]),
[iquote('0:SpR:512.0,7.0')] ).
cnf(864,plain,
equal(mult(mult(op_a,mult(op_a,op_a)),mult(op_b,op_b)),op_a),
inference(rew,[status(thm),theory(equality)],[493,861]),
[iquote('0:Rew:493.0,861.0')] ).
cnf(1580,plain,
equal(mult(mult(mult(u,op_b),op_a),mult(op_b,op_b)),mult(mult(u,mult(unit,op_b)),op_b)),
inference(spr,[status(thm),theory(equality)],[11,157]),
[iquote('0:SpR:11.0,157.0')] ).
cnf(1596,plain,
equal(mult(mult(u,mult(mult(op_a,op_a),op_b)),op_b),mult(mult(mult(u,op_b),mult(op_a,mult(op_a,op_a))),mult(op_b,op_b))),
inference(spr,[status(thm),theory(equality)],[374,157]),
[iquote('0:SpR:374.0,157.0')] ).
cnf(1662,plain,
equal(mult(mult(mult(u,op_b),op_a),mult(op_b,op_b)),mult(u,mult(op_b,op_b))),
inference(rew,[status(thm),theory(equality)],[7,1580,9]),
[iquote('0:Rew:7.0,1580.0,9.0,1580.0')] ).
cnf(1699,plain,
equal(mult(mult(mult(u,op_b),mult(op_a,mult(op_a,op_a))),mult(op_b,op_b)),mult(mult(u,op_a),op_b)),
inference(rew,[status(thm),theory(equality)],[493,1596]),
[iquote('0:Rew:493.0,1596.0')] ).
cnf(1833,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,op_a))),op_b),mult(mult(u,mult(op_a,op_a)),mult(mult(op_b,mult(op_a,op_a)),op_b))),
inference(spr,[status(thm),theory(equality)],[493,162]),
[iquote('0:SpR:493.0,162.0')] ).
cnf(1845,plain,
equal(mult(mult(u,mult(op_a,op_b)),mult(op_a,op_a)),mult(mult(u,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a)))),
inference(spr,[status(thm),theory(equality)],[41,162]),
[iquote('0:SpR:41.0,162.0')] ).
cnf(1851,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(mult(u,mult(op_a,mult(op_a,op_a))),mult(mult(mult(op_b,op_b),mult(op_a,mult(op_a,op_a))),mult(op_b,op_b)))),
inference(spr,[status(thm),theory(equality)],[864,162]),
[iquote('0:SpR:864.0,162.0')] ).
cnf(1907,plain,
equal(mult(mult(u,op_b),mult(op_a,mult(op_a,op_a))),mult(u,mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[8,1845,10,493]),
[iquote('0:Rew:8.0,1845.0,10.0,1845.0,493.0,1845.0')] ).
cnf(1909,plain,
equal(mult(mult(u,mult(op_a,op_a)),mult(op_b,op_b)),mult(mult(u,op_a),op_b)),
inference(rew,[status(thm),theory(equality)],[1907,1699]),
[iquote('0:Rew:1907.0,1699.0')] ).
cnf(1915,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,op_a))),op_b),mult(u,mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[8,1833,10,41]),
[iquote('0:Rew:8.0,1833.0,10.0,1833.0,41.0,1833.0')] ).
cnf(1954,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(mult(u,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,op_a),op_b))),
inference(rew,[status(thm),theory(equality)],[1909,1851,1907]),
[iquote('0:Rew:1909.0,1851.0,1907.0,1851.0')] ).
cnf(1955,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(mult(u,mult(op_a,mult(op_a,op_a))),op_b)),
inference(rew,[status(thm),theory(equality)],[9,1954,11]),
[iquote('0:Rew:9.0,1954.0,11.0,1954.0')] ).
cnf(1956,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(u,mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[1915,1955]),
[iquote('0:Rew:1915.0,1955.0')] ).
cnf(6376,plain,
equal(mult(mult(u,mult(mult(op_a,mult(op_a,op_a)),op_b)),op_b),mult(mult(mult(u,op_b),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b))),
inference(spr,[status(thm),theory(equality)],[181,157]),
[iquote('0:SpR:181.0,157.0')] ).
cnf(6381,plain,
equal(mult(mult(mult(u,op_b),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(mult(u,mult(op_a,op_a)),op_b)),
inference(rew,[status(thm),theory(equality)],[512,6376]),
[iquote('0:Rew:512.0,6376.0')] ).
cnf(6382,plain,
equal(mult(mult(u,mult(op_a,op_a)),op_b),mult(mult(u,op_b),mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[1956,6381]),
[iquote('0:Rew:1956.0,6381.0')] ).
cnf(7267,plain,
equal(mult(mult(u,mult(op_b,op_b)),op_a),mult(mult(u,op_b),mult(mult(op_a,mult(op_b,op_b)),op_a))),
inference(spr,[status(thm),theory(equality)],[1662,6]),
[iquote('0:SpR:1662.0,6.0')] ).
cnf(7298,plain,
equal(mult(mult(u,mult(op_b,op_b)),op_a),mult(u,op_b)),
inference(rew,[status(thm),theory(equality)],[8,7267,11,42]),
[iquote('0:Rew:8.0,7267.0,11.0,7267.0,42.0,7267.0')] ).
cnf(7364,plain,
equal(mult(mult(u,op_a),op_b),mult(u,mult(mult(op_a,mult(op_b,op_b)),op_a))),
inference(spr,[status(thm),theory(equality)],[7298,6]),
[iquote('0:SpR:7298.0,6.0')] ).
cnf(7365,plain,
equal(mult(mult(u,mult(op_a,op_a)),op_b),mult(mult(u,op_a),mult(mult(op_a,mult(op_b,op_b)),op_a))),
inference(spr,[status(thm),theory(equality)],[7298,168]),
[iquote('0:SpR:7298.0,168.0')] ).
cnf(7398,plain,
equal(mult(mult(u,op_a),op_b),u),
inference(rew,[status(thm),theory(equality)],[8,7364,11,42]),
[iquote('0:Rew:8.0,7364.0,11.0,7364.0,42.0,7364.0')] ).
cnf(7469,plain,
equal(mult(mult(u,mult(op_a,op_a)),op_b),mult(u,op_a)),
inference(rew,[status(thm),theory(equality)],[8,7365,11,42]),
[iquote('0:Rew:8.0,7365.0,11.0,7365.0,42.0,7365.0')] ).
cnf(7470,plain,
equal(mult(mult(u,op_b),mult(op_a,op_a)),mult(u,op_a)),
inference(rew,[status(thm),theory(equality)],[6382,7469]),
[iquote('0:Rew:6382.0,7469.0')] ).
cnf(7474,plain,
equal(mult(mult(u,mult(op_a,op_a)),op_b),mult(u,op_a)),
inference(rew,[status(thm),theory(equality)],[7470,6382]),
[iquote('0:Rew:7470.0,6382.0')] ).
cnf(7980,plain,
equal(mult(mult(u,op_b),op_a),mult(mult(u,op_a),op_b)),
inference(spr,[status(thm),theory(equality)],[7470,7474]),
[iquote('0:SpR:7470.0,7474.0')] ).
cnf(7987,plain,
equal(mult(mult(u,op_b),op_a),u),
inference(rew,[status(thm),theory(equality)],[7398,7980]),
[iquote('0:Rew:7398.0,7980.0')] ).
cnf(7988,plain,
$false,
inference(unc,[status(thm)],[7987,12]),
[iquote('0:UnC:7987.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP715-11 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 13:49:58 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.44/2.60
% 2.44/2.60 SPASS V 3.9
% 2.44/2.60 SPASS beiseite: Proof found.
% 2.44/2.60 % SZS status Theorem
% 2.44/2.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.44/2.60 SPASS derived 4497 clauses, backtracked 0 clauses, performed 0 splits and kept 1352 clauses.
% 2.44/2.60 SPASS allocated 76587 KBytes.
% 2.44/2.60 SPASS spent 0:00:02.17 on the problem.
% 2.44/2.60 0:00:00.03 for the input.
% 2.44/2.60 0:00:00.00 for the FLOTTER CNF translation.
% 2.44/2.60 0:00:00.05 for inferences.
% 2.44/2.60 0:00:00.00 for the backtracking.
% 2.44/2.60 0:00:02.07 for the reduction.
% 2.44/2.60
% 2.44/2.60
% 2.44/2.60 Here is a proof with depth 5, length 56 :
% 2.44/2.60 % SZS output start Refutation
% See solution above
% 2.44/2.60 Formulae used in the proof : f06 f07 f08 f09 f10 f11 goal
% 2.44/2.60
%------------------------------------------------------------------------------