TSTP Solution File: SYN077-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN077-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 21 12:18:23 EDT 2022
% Result : Unsatisfiable 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of clauses : 31 ( 3 unt; 7 nHn; 31 RR)
% Number of literals : 97 ( 0 equ; 68 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ big(u,f(v))
| equal(u,v) ),
file('SYN077-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(u,v)
| big(u,f(v)) ),
file('SYN077-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ big(u,v)
| ~ big(u,a)
| big(g(u,v),v) ),
file('SYN077-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ big(u,v)
| ~ big(w,v)
| ~ big(w,a)
| ~ big(u,g(w,v)) ),
file('SYN077-1.p',unknown),
[] ).
cnf(5,axiom,
( big(u,a)
| big(u,h(u)) ),
file('SYN077-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ big(u,h(v))
| big(v,a)
| big(i(v,u),u) ),
file('SYN077-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ big(u,h(v))
| big(v,a)
| big(i(v,u),h(v)) ),
file('SYN077-1.p',unknown),
[] ).
cnf(10,plain,
( ~ big(u,f(v))
| ~ big(u,a)
| equal(g(u,f(v)),v) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.2,1.0')] ).
cnf(21,plain,
( ~ big(g(u,v),h(w))
| ~ big(i(w,g(u,v)),v)
| ~ big(u,v)
| ~ big(u,a)
| big(w,a) ),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.2,4.3')] ).
cnf(35,plain,
( ~ big(u,f(v))
| ~ big(u,a)
| ~ big(u,f(v))
| ~ big(u,a)
| big(v,f(v)) ),
inference(spr,[status(thm),theory(equality)],[10,3]),
[iquote('0:SpR:10.2,3.2')] ).
cnf(37,plain,
( ~ big(u,f(v))
| ~ big(u,a)
| ~ big(w,f(v))
| ~ big(u,f(v))
| ~ big(u,a)
| ~ big(w,v) ),
inference(spl,[status(thm),theory(equality)],[10,4]),
[iquote('0:SpL:10.2,4.3')] ).
cnf(38,plain,
( ~ big(u,f(v))
| ~ big(u,a)
| big(v,f(v)) ),
inference(obv,[status(thm),theory(equality)],[35]),
[iquote('0:Obv:35.1')] ).
cnf(39,plain,
( ~ big(u,f(v))
| ~ big(w,f(v))
| ~ big(w,a)
| ~ big(u,v) ),
inference(obv,[status(thm),theory(equality)],[37]),
[iquote('0:Obv:37.1')] ).
cnf(40,plain,
( ~ equal(u,v)
| ~ big(u,a)
| big(v,f(v)) ),
inference(res,[status(thm),theory(equality)],[2,38]),
[iquote('0:Res:2.1,38.0')] ).
cnf(46,plain,
( ~ big(u,a)
| big(u,f(u)) ),
inference(eqr,[status(thm),theory(equality)],[40]),
[iquote('0:EqR:40.0')] ).
cnf(77,plain,
( ~ big(g(u,h(v)),h(v))
| ~ big(g(u,h(v)),h(v))
| ~ big(u,h(v))
| ~ big(u,a)
| big(v,a)
| big(v,a) ),
inference(res,[status(thm),theory(equality)],[7,21]),
[iquote('0:Res:7.2,21.1')] ).
cnf(79,plain,
( ~ big(g(u,h(v)),h(v))
| ~ big(u,h(v))
| ~ big(u,a)
| big(v,a) ),
inference(obv,[status(thm),theory(equality)],[77]),
[iquote('0:Obv:77.4')] ).
cnf(80,plain,
( ~ big(u,h(v))
| ~ big(u,a)
| big(v,a) ),
inference(mrr,[status(thm)],[79,3]),
[iquote('0:MRR:79.0,3.2')] ).
cnf(88,plain,
( ~ big(u,h(v))
| ~ big(i(v,u),a)
| big(v,a)
| big(v,a) ),
inference(res,[status(thm),theory(equality)],[7,80]),
[iquote('0:Res:7.2,80.0')] ).
cnf(93,plain,
( ~ big(u,h(v))
| ~ big(i(v,u),a)
| big(v,a) ),
inference(obv,[status(thm),theory(equality)],[88]),
[iquote('0:Obv:88.2')] ).
cnf(101,plain,
( ~ big(u,f(v))
| ~ big(u,a)
| ~ big(w,f(v))
| ~ big(w,a)
| ~ big(g(u,f(v)),v) ),
inference(res,[status(thm),theory(equality)],[3,39]),
[iquote('0:Res:3.2,39.0')] ).
cnf(102,plain,
( ~ big(u,f(v))
| ~ big(u,a)
| ~ big(g(u,f(v)),v) ),
inference(con,[status(thm)],[101]),
[iquote('0:Con:101.2')] ).
cnf(103,plain,
( ~ big(u,f(v))
| ~ big(u,a)
| ~ big(v,v) ),
inference(rew,[status(thm),theory(equality)],[10,102]),
[iquote('0:Rew:10.2,102.2')] ).
cnf(108,plain,
( ~ big(u,a)
| ~ big(u,a)
| ~ big(u,u) ),
inference(res,[status(thm),theory(equality)],[46,103]),
[iquote('0:Res:46.1,103.0')] ).
cnf(113,plain,
( ~ big(u,a)
| ~ big(u,u) ),
inference(obv,[status(thm),theory(equality)],[108]),
[iquote('0:Obv:108.0')] ).
cnf(183,plain,
( ~ big(a,h(u))
| ~ big(a,h(u))
| big(u,a)
| big(u,a) ),
inference(res,[status(thm),theory(equality)],[6,93]),
[iquote('0:Res:6.2,93.1')] ).
cnf(184,plain,
( ~ big(a,h(u))
| big(u,a) ),
inference(obv,[status(thm),theory(equality)],[183]),
[iquote('0:Obv:183.2')] ).
cnf(190,plain,
( big(a,a)
| big(a,a) ),
inference(res,[status(thm),theory(equality)],[5,184]),
[iquote('0:Res:5.1,184.0')] ).
cnf(194,plain,
big(a,a),
inference(obv,[status(thm),theory(equality)],[190]),
[iquote('0:Obv:190.0')] ).
cnf(199,plain,
~ big(a,a),
inference(res,[status(thm),theory(equality)],[194,113]),
[iquote('0:Res:194.0,113.0')] ).
cnf(200,plain,
$false,
inference(mrr,[status(thm)],[199,194]),
[iquote('0:MRR:199.0,194.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYN077-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.16/0.36 % Computer : n006.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Mon Jul 11 22:43:35 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.22/0.45
% 0.22/0.45 SPASS V 3.9
% 0.22/0.45 SPASS beiseite: Proof found.
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.45 SPASS derived 122 clauses, backtracked 0 clauses, performed 0 splits and kept 84 clauses.
% 0.22/0.45 SPASS allocated 63258 KBytes.
% 0.22/0.45 SPASS spent 0:00:00.07 on the problem.
% 0.22/0.45 0:00:00.03 for the input.
% 0.22/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.45 0:00:00.00 for inferences.
% 0.22/0.45 0:00:00.00 for the backtracking.
% 0.22/0.45 0:00:00.01 for the reduction.
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 Here is a proof with depth 6, length 31 :
% 0.22/0.45 % SZS output start Refutation
% See solution above
% 0.22/0.45 Formulae used in the proof : clause_1 clause_2 clause_3 clause_4 clause_5 clause_6 clause_7
% 0.22/0.45
%------------------------------------------------------------------------------