TSTP Solution File: COL121-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL121-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : Fri Jul 15 00:42:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.55s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 4 unt; 0 nHn; 23 RR)
% Number of literals : 57 ( 0 equ; 40 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_Comb_Odiamond(u,v)
| ~ c_in(c_Pair(w,x,v,v),u,tc_prod(v,v))
| ~ c_in(c_Pair(w,y,v,v),c_Transitive__Closure_Ortrancl(u,v),tc_prod(v,v))
| c_in(c_Pair(x,c_Comb_Odiamond__strip__lemmaE__1(u,y,x,v),v,v),c_Transitive__Closure_Ortrancl(u,v),tc_prod(v,v)) ),
file('COL121-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_Comb_Odiamond(u,v)
| ~ c_in(c_Pair(w,x,v,v),u,tc_prod(v,v))
| ~ c_in(c_Pair(w,y,v,v),c_Transitive__Closure_Ortrancl(u,v),tc_prod(v,v))
| c_in(c_Pair(y,c_Comb_Odiamond__strip__lemmaE__1(u,y,x,v),v,v),u,tc_prod(v,v)) ),
file('COL121-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,v,tc_prod(w,w))
| c_in(u,c_Transitive__Closure_Ortrancl(v,w),tc_prod(w,w)) ),
file('COL121-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(c_Pair(u,v,w,w),c_Transitive__Closure_Ortrancl(x,w),tc_prod(w,w))
| ~ c_in(c_Pair(v,y,w,w),c_Transitive__Closure_Ortrancl(x,w),tc_prod(w,w))
| c_in(c_Pair(u,y,w,w),c_Transitive__Closure_Ortrancl(x,w),tc_prod(w,w)) ),
file('COL121-2.p',unknown),
[] ).
cnf(5,axiom,
c_Comb_Odiamond(v_r,t_a),
file('COL121-2.p',unknown),
[] ).
cnf(6,axiom,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('COL121-2.p',unknown),
[] ).
cnf(7,axiom,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('COL121-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(u),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('COL121-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(u,v_x(u),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('COL121-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ c_in(c_Pair(v_z,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('COL121-2.p',unknown),
[] ).
cnf(18,plain,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(u),v,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(u,v,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[9,4]),
[iquote('0:Res:9.1,4.0')] ).
cnf(26,plain,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(u),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(u),v,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.1,2.2')] ).
cnf(32,plain,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_x(u),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(u),v,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(mrr,[status(thm)],[26,5]),
[iquote('0:MRR:26.1,5.0')] ).
cnf(36,plain,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a)
| ~ c_in(c_Pair(v_ya,v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(u),v,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.1,1.2')] ).
cnf(42,plain,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(u),v,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(mrr,[status(thm)],[36,5]),
[iquote('0:MRR:36.1,5.0')] ).
cnf(97,plain,
( ~ c_in(c_Pair(v_x(u),v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(u,v,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[3,18]),
[iquote('0:Res:3.1,18.1')] ).
cnf(184,plain,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(u),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[42,10]),
[iquote('0:Res:42.2,10.0')] ).
cnf(195,plain,
( ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(u),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(mrr,[status(thm)],[184,6]),
[iquote('0:MRR:184.1,6.0')] ).
cnf(486,plain,
( ~ c_in(c_Pair(v_x(v_xaa),u,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[7,97]),
[iquote('0:Res:7.0,97.1')] ).
cnf(515,plain,
( ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(u),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[486,195]),
[iquote('0:Res:486.1,195.1')] ).
cnf(705,plain,
( ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[32,515]),
[iquote('0:Res:32.2,515.0')] ).
cnf(707,plain,
( ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(obv,[status(thm),theory(equality)],[705]),
[iquote('0:Obv:705.0')] ).
cnf(708,plain,
$false,
inference(mrr,[status(thm)],[707,6,7]),
[iquote('0:MRR:707.0,707.1,6.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL121-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.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 : Tue May 31 15:42:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.55
% 0.19/0.55 SPASS V 3.9
% 0.19/0.55 SPASS beiseite: Proof found.
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.55 SPASS derived 581 clauses, backtracked 0 clauses, performed 0 splits and kept 483 clauses.
% 0.19/0.55 SPASS allocated 63941 KBytes.
% 0.19/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.19/0.55 0:00:00.03 for the input.
% 0.19/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.55 0:00:00.02 for inferences.
% 0.19/0.55 0:00:00.00 for the backtracking.
% 0.19/0.55 0:00:00.12 for the reduction.
% 0.19/0.55
% 0.19/0.55
% 0.19/0.55 Here is a proof with depth 5, length 23 :
% 0.19/0.55 % SZS output start Refutation
% See solution above
% 0.19/0.55 Formulae used in the proof : cls_Comb_Odiamond__strip__lemmaE_0 cls_Comb_Odiamond__strip__lemmaE_1 cls_Transitive__Closure_Or__into__rtrancl_0 cls_Transitive__Closure_Ortrancl__trans_0 cls_conjecture_0 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_conjecture_6
% 0.19/0.55
%------------------------------------------------------------------------------