TSTP Solution File: COL123-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL123-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 0.57s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 3 unt; 0 nHn; 18 RR)
% Number of literals : 42 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 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_in(u,v,tc_prod(w,w))
| c_in(u,c_Transitive__Closure_Ortrancl(v,w),tc_prod(w,w)) ),
file('COL123-2.p',unknown),
[] ).
cnf(2,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('COL123-2.p',unknown),
[] ).
cnf(3,axiom,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('COL123-2.p',unknown),
[] ).
cnf(4,axiom,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('COL123-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(c_Pair(v_x,u,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(u,v_xaa(u),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('COL123-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(c_Pair(v_x,u,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_xaa(u),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('COL123-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_in(c_Pair(v_z,u,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xb,u,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('COL123-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ c_in(c_Pair(u,v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(u,w,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v,v_xa(u,v,w),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('COL123-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ c_in(c_Pair(u,v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(u,w,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(w,v_xa(u,v,w),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('COL123-2.p',unknown),
[] ).
cnf(20,plain,
( ~ c_in(c_Pair(v_x,u,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa(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)],[5,2]),
[iquote('0:Res:5.1,2.0')] ).
cnf(37,plain,
( ~ c_in(c_Pair(v_xaa(u),v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,u,t_a,t_a),v_r,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)],[1,20]),
[iquote('0:Res:1.1,20.1')] ).
cnf(60,plain,
( ~ c_in(c_Pair(v_xaa(v_xb),u,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,u,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[37,7]),
[iquote('0:Res:37.2,7.1')] ).
cnf(65,plain,
( ~ c_in(c_Pair(v_xaa(v_xb),u,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,u,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(mrr,[status(thm)],[60,4]),
[iquote('0:MRR:60.1,4.0')] ).
cnf(67,plain,
( ~ c_in(c_Pair(u,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(u,v,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,v_xa(u,v_xaa(v_xb),v),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[8,65]),
[iquote('0:Res:8.2,65.0')] ).
cnf(523,plain,
( ~ c_in(c_Pair(u,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(u,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(u,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(u,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[9,67]),
[iquote('0:Res:9.2,67.2')] ).
cnf(524,plain,
( ~ c_in(c_Pair(u,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(u,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(obv,[status(thm),theory(equality)],[523]),
[iquote('0:Obv:523.1')] ).
cnf(525,plain,
( ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(res,[status(thm),theory(equality)],[6,524]),
[iquote('0:Res:6.1,524.0')] ).
cnf(526,plain,
$false,
inference(mrr,[status(thm)],[525,4,3]),
[iquote('0:MRR:525.0,525.1,4.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL123-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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 : Tue May 31 10:07:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.57
% 0.19/0.57 SPASS V 3.9
% 0.19/0.57 SPASS beiseite: Proof found.
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.57 SPASS derived 499 clauses, backtracked 0 clauses, performed 0 splits and kept 412 clauses.
% 0.19/0.57 SPASS allocated 63688 KBytes.
% 0.19/0.57 SPASS spent 0:00:00.22 on the problem.
% 0.19/0.57 0:00:00.04 for the input.
% 0.19/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.57 0:00:00.02 for inferences.
% 0.19/0.57 0:00:00.00 for the backtracking.
% 0.19/0.57 0:00:00.14 for the reduction.
% 0.19/0.57
% 0.19/0.57
% 0.19/0.57 Here is a proof with depth 6, length 18 :
% 0.19/0.57 % SZS output start Refutation
% See solution above
% 0.19/0.57 Formulae used in the proof : cls_Transitive__Closure_Or__into__rtrancl_0 cls_Transitive__Closure_Ortrancl__trans_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_conjecture_6 cls_conjecture_7
% 0.19/0.57
%------------------------------------------------------------------------------