TSTP Solution File: SYO691-1.001 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYO691-1.001 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 19:55:35 EDT 2022
% Result : Unsatisfiable 6.50s 6.70s
% Output : Refutation 6.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of clauses : 28 ( 5 unt; 0 nHn; 28 RR)
% Number of literals : 71 ( 0 equ; 53 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
top(f(f(f(u,a),v),f(w,a)),f(f(w,f(f(v,a),a)),u)),
file('SYO691-1.001.p',unknown),
[] ).
cnf(2,axiom,
( ~ top(u,v)
| step__dfg(u,v) ),
file('SYO691-1.001.p',unknown),
[] ).
cnf(3,axiom,
( ~ step__dfg(u,v)
| step__dfg(f(u,w),f(v,w)) ),
file('SYO691-1.001.p',unknown),
[] ).
cnf(4,axiom,
( ~ step__dfg(u,v)
| step__dfg(f(w,u),f(w,v)) ),
file('SYO691-1.001.p',unknown),
[] ).
cnf(5,axiom,
seq(zero,u,u),
file('SYO691-1.001.p',unknown),
[] ).
cnf(6,axiom,
( ~ step__dfg(u,v)
| ~ seq(w,x,u)
| seq(succ(w),x,v) ),
file('SYO691-1.001.p',unknown),
[] ).
cnf(7,axiom,
~ seq(succ(succ(succ(succ(succ(zero))))),u,u),
file('SYO691-1.001.p',unknown),
[] ).
cnf(8,plain,
( ~ step__dfg(u,v)
| ~ seq(succ(succ(succ(succ(zero)))),v,u) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.2,7.0')] ).
cnf(9,plain,
( ~ step__dfg(u,v)
| seq(succ(zero),u,v) ),
inference(res,[status(thm),theory(equality)],[5,6]),
[iquote('0:Res:5.0,6.1')] ).
cnf(10,plain,
( ~ step__dfg(u,v)
| ~ step__dfg(v,w)
| seq(succ(succ(zero)),u,w) ),
inference(res,[status(thm),theory(equality)],[9,6]),
[iquote('0:Res:9.1,6.1')] ).
cnf(12,plain,
( ~ step__dfg(u,v)
| ~ step__dfg(f(w,v),x)
| seq(succ(succ(zero)),f(w,u),x) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.1,10.0')] ).
cnf(17,plain,
( ~ step__dfg(u,v)
| ~ step__dfg(w,x)
| seq(succ(succ(zero)),f(u,w),f(v,x)) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.1,12.1')] ).
cnf(25,plain,
( ~ step__dfg(u,v)
| ~ step__dfg(w,x)
| ~ step__dfg(f(v,x),y)
| seq(succ(succ(succ(zero))),f(u,w),y) ),
inference(res,[status(thm),theory(equality)],[17,6]),
[iquote('0:Res:17.2,6.1')] ).
cnf(53,plain,
( ~ top(f(u,v),w)
| ~ step__dfg(x,u)
| ~ step__dfg(y,v)
| seq(succ(succ(succ(zero))),f(x,y),w) ),
inference(res,[status(thm),theory(equality)],[2,25]),
[iquote('0:Res:2.1,25.2')] ).
cnf(81,plain,
( ~ step__dfg(u,f(f(v,a),w))
| ~ step__dfg(x,f(y,a))
| seq(succ(succ(succ(zero))),f(u,x),f(f(y,f(f(w,a),a)),v)) ),
inference(res,[status(thm),theory(equality)],[1,53]),
[iquote('0:Res:1.0,53.0')] ).
cnf(225,plain,
( ~ step__dfg(u,f(f(v,a),w))
| ~ step__dfg(x,f(y,a))
| ~ step__dfg(f(f(y,f(f(w,a),a)),v),z)
| seq(succ(succ(succ(succ(zero)))),f(u,x),z) ),
inference(res,[status(thm),theory(equality)],[81,6]),
[iquote('0:Res:81.2,6.1')] ).
cnf(632,plain,
( ~ step__dfg(f(u,f(f(v,a),a)),w)
| ~ step__dfg(x,f(f(y,a),v))
| ~ step__dfg(z,f(u,a))
| seq(succ(succ(succ(succ(zero)))),f(x,z),f(w,y)) ),
inference(res,[status(thm),theory(equality)],[3,225]),
[iquote('0:Res:3.1,225.2')] ).
cnf(1081,plain,
( ~ top(f(u,f(f(v,a),a)),w)
| ~ step__dfg(x,f(f(y,a),v))
| ~ step__dfg(z,f(u,a))
| seq(succ(succ(succ(succ(zero)))),f(x,z),f(w,y)) ),
inference(res,[status(thm),theory(equality)],[2,632]),
[iquote('0:Res:2.1,632.0')] ).
cnf(1461,plain,
( ~ step__dfg(u,f(f(v,a),w))
| ~ step__dfg(x,f(f(f(y,a),z),a))
| seq(succ(succ(succ(succ(zero)))),f(u,x),f(f(f(f(w,a),f(f(z,a),a)),y),v)) ),
inference(res,[status(thm),theory(equality)],[1,1081]),
[iquote('0:Res:1.0,1081.0')] ).
cnf(3737,plain,
( ~ step__dfg(u,f(f(v,a),w))
| ~ step__dfg(x,f(f(f(y,a),z),a))
| ~ step__dfg(f(f(f(f(w,a),f(f(z,a),a)),y),v),f(u,x)) ),
inference(res,[status(thm),theory(equality)],[1461,8]),
[iquote('0:Res:1461.2,8.1')] ).
cnf(3740,plain,
( ~ step__dfg(u,v)
| ~ step__dfg(f(f(f(w,a),f(f(x,a),a)),y),f(f(u,a),w))
| ~ step__dfg(v,f(f(f(y,a),x),a)) ),
inference(res,[status(thm),theory(equality)],[4,3737]),
[iquote('0:Res:4.1,3737.2')] ).
cnf(3746,plain,
( ~ step__dfg(f(f(u,a),f(f(v,a),a)),f(w,a))
| ~ step__dfg(w,x)
| ~ step__dfg(x,f(f(f(u,a),v),a)) ),
inference(res,[status(thm),theory(equality)],[3,3740]),
[iquote('0:Res:3.1,3740.1')] ).
cnf(3747,plain,
( ~ top(f(f(u,a),f(f(v,a),a)),f(w,a))
| ~ step__dfg(w,x)
| ~ step__dfg(x,f(f(f(u,a),v),a)) ),
inference(res,[status(thm),theory(equality)],[2,3746]),
[iquote('0:Res:2.1,3746.0')] ).
cnf(3751,plain,
( ~ step__dfg(f(f(u,a),f(f(a,a),a)),v)
| ~ step__dfg(v,f(f(f(f(a,a),a),u),a)) ),
inference(res,[status(thm),theory(equality)],[1,3747]),
[iquote('0:Res:1.0,3747.0')] ).
cnf(3752,plain,
( ~ top(f(f(u,a),f(f(a,a),a)),v)
| ~ step__dfg(v,f(f(f(f(a,a),a),u),a)) ),
inference(res,[status(thm),theory(equality)],[2,3751]),
[iquote('0:Res:2.1,3751.0')] ).
cnf(3762,plain,
( ~ top(u,f(f(f(f(a,a),a),v),a))
| ~ top(f(f(v,a),f(f(a,a),a)),u) ),
inference(res,[status(thm),theory(equality)],[2,3752]),
[iquote('0:Res:2.1,3752.1')] ).
cnf(3767,plain,
~ top(f(f(f(f(u,a),a),a),f(f(a,a),a)),f(f(f(a,a),u),f(f(f(a,a),a),a))),
inference(res,[status(thm),theory(equality)],[1,3762]),
[iquote('0:Res:1.0,3762.0')] ).
cnf(3768,plain,
$false,
inference(unc,[status(thm)],[3767,1]),
[iquote('0:UnC:3767.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO691-1.001 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 13:29:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.50/6.70
% 6.50/6.70 SPASS V 3.9
% 6.50/6.70 SPASS beiseite: Proof found.
% 6.50/6.70 % SZS status Theorem
% 6.50/6.70 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.50/6.70 SPASS derived 3737 clauses, backtracked 0 clauses, performed 0 splits and kept 3321 clauses.
% 6.50/6.70 SPASS allocated 70666 KBytes.
% 6.50/6.70 SPASS spent 0:00:06.30 on the problem.
% 6.50/6.70 0:00:00.03 for the input.
% 6.50/6.70 0:00:00.00 for the FLOTTER CNF translation.
% 6.50/6.70 0:00:00.45 for inferences.
% 6.50/6.70 0:00:00.00 for the backtracking.
% 6.50/6.70 0:00:05.45 for the reduction.
% 6.50/6.70
% 6.50/6.70
% 6.50/6.70 Here is a proof with depth 19, length 28 :
% 6.50/6.70 % SZS output start Refutation
% See solution above
% 6.50/6.70 Formulae used in the proof : rule_1 rewrite_top rewrite_left rewrite_right rewrite_sequence_zero rewrite_sequence_succ prove
% 6.50/6.70
%------------------------------------------------------------------------------