TSTP Solution File: COL104-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL104-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 00:42:39 EDT 2022
% Result : Unsatisfiable 0.15s 0.35s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 6 unt; 0 nHn; 11 RR)
% Number of literals : 17 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(c_Pair(u,v,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(w,u),c_Comb_Ocomb_Oop_A_D_D(w,v),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('COL104-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v,tc_prod(w,w))
| c_in(u,c_Transitive__Closure_Ortrancl(v,w),tc_prod(w,w)) ),
file('COL104-2.p',unknown),
[] ).
cnf(3,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('COL104-2.p',unknown),
[] ).
cnf(4,axiom,
c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('COL104-2.p',unknown),
[] ).
cnf(5,axiom,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),c_Comb_Ocomb_Oop_A_D_D(v_z,v_y),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('COL104-2.p',unknown),
[] ).
cnf(6,axiom,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),c_Comb_Ocomb_Oop_A_D_D(v_z,v_za),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('COL104-2.p',unknown),
[] ).
cnf(7,plain,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(u,v_y),c_Comb_Ocomb_Oop_A_D_D(u,v_za),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.0')] ).
cnf(11,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_y),u,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),u,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.0,3.1')] ).
cnf(21,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_y),u,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),u,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.1,11.0')] ).
cnf(22,plain,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_y),c_Comb_Ocomb_Oop_A_D_D(v_z,v_za),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(res,[status(thm),theory(equality)],[21,6]),
[iquote('0:Res:21.1,6.0')] ).
cnf(24,plain,
$false,
inference(mrr,[status(thm)],[22,7]),
[iquote('0:MRR:22.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : COL104-2 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.11 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Tue May 31 15:02:13 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.35
% 0.15/0.35 SPASS V 3.9
% 0.15/0.35 SPASS beiseite: Proof found.
% 0.15/0.35 % SZS status Theorem
% 0.15/0.35 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35 SPASS derived 17 clauses, backtracked 0 clauses, performed 0 splits and kept 21 clauses.
% 0.15/0.35 SPASS allocated 63129 KBytes.
% 0.15/0.35 SPASS spent 0:00:00.04 on the problem.
% 0.15/0.35 0:00:00.02 for the input.
% 0.15/0.35 0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.35 0:00:00.00 for inferences.
% 0.15/0.35 0:00:00.00 for the backtracking.
% 0.15/0.35 0:00:00.00 for the reduction.
% 0.15/0.35
% 0.15/0.35
% 0.15/0.35 Here is a proof with depth 3, length 11 :
% 0.15/0.35 % SZS output start Refutation
% See solution above
% 0.15/0.35 Formulae used in the proof : cls_Comb_Ocontract_OAp2_0 cls_Transitive__Closure_Or__into__rtrancl_0 cls_Transitive__Closure_Ortrancl__trans_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.15/0.35
%------------------------------------------------------------------------------