%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL123-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %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 00:36:33 EDT 2022
% Result : Unsatisfiable 33.28s 33.45s
% Output : CNFRefutation 33.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 10 unt; 0 nHn; 30 RR)
% Number of literals : 56 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Transitive__Closure_Or__into__rtrancl_0,axiom,
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).
cnf(cls_Transitive__Closure_Ortrancl__trans_0,axiom,
( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_in(c_Pair(V_U,v_xaa(V_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,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_in(c_Pair(v_y,v_xaa(V_U),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( ~ c_in(c_Pair(v_z,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xb,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_in(c_Pair(V_V,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U,V_W,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ).
cnf(cls_conjecture_7,negated_conjecture,
( c_in(c_Pair(V_W,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U,V_W,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ).
cnf(refute_0_0,plain,
( ~ c_in(c_Pair(v_xb,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_conjecture_5:[bind(V_U,$fot(v_xa(v_y,v_xaa(v_xb),v_z)))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xb,v_xaa(v_xb),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_conjecture_3:[bind(V_U,$fot(v_xb))]]) ).
cnf(refute_0_2,plain,
c_in(c_Pair(v_xb,v_xaa(v_xb),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[cls_conjecture_2,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Transitive__Closure_Or__into__rtrancl_0:[bind(T_a,$fot(t_a)),bind(V_p,$fot(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a))),bind(V_r,$fot(v_r))]]) ).
cnf(refute_0_4,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_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_conjecture_4:[bind(V_U,$fot(v_xb))]]) ).
cnf(refute_0_5,plain,
c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[cls_conjecture_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ c_in(c_Pair(v_y,X_10,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),X_10),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_conjecture_6:[bind(V_U,$fot(v_y)),bind(V_V,$fot(v_xaa(v_xb))),bind(V_W,$fot(X_10))]]) ).
cnf(refute_0_7,plain,
( ~ c_in(c_Pair(v_y,X_10,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),X_10),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(v_z))]]) ).
cnf(refute_0_9,plain,
c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[cls_conjecture_1,refute_0_8]) ).
cnf(refute_0_10,plain,
c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_9,refute_0_3]) ).
cnf(refute_0_11,plain,
( ~ c_in(c_Pair(X_99,v_xaa(v_xb),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X_99,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Transitive__Closure_Ortrancl__trans_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_99)),bind(V_b,$fot(v_xaa(v_xb))),bind(V_c,$fot(v_xa(v_y,v_xaa(v_xb),v_z))),bind(V_r,$fot(v_r))]]) ).
cnf(refute_0_12,plain,
( ~ c_in(c_Pair(X_99,v_xaa(v_xb),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X_99,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ c_in(c_Pair(v_xb,v_xaa(v_xb),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_xb,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_12:[bind(X_99,$fot(v_xb))]]) ).
cnf(refute_0_14,plain,
c_in(c_Pair(v_xb,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(v_xb,v_xaa(v_xb),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
~ c_in(c_Pair(v_z,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(v_xb,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
( ~ c_in(c_Pair(v_y,X_32,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(X_32,v_xa(v_y,v_xaa(v_xb),X_32),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_conjecture_7:[bind(V_U,$fot(v_y)),bind(V_V,$fot(v_xaa(v_xb))),bind(V_W,$fot(X_32))]]) ).
cnf(refute_0_17,plain,
( ~ c_in(c_Pair(v_y,X_32,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(X_32,v_xa(v_y,v_xaa(v_xb),X_32),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_5,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_z,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_17:[bind(X_32,$fot(v_z))]]) ).
cnf(refute_0_19,plain,
c_in(c_Pair(v_z,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[cls_conjecture_1,refute_0_18]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( c_in(c_Pair(v_z,v_xa(v_y,v_xaa(v_xb),v_z),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_19,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COL123-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %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 10:06:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 33.28/33.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.28/33.45
% 33.28/33.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.28/33.46
%------------------------------------------------------------------------------