TSTP Solution File: COL121-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL121-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 : 300s
% DateTime : Wed Jul 27 12:48:17 EDT 2022
% Result : Unsatisfiable 1.72s 1.94s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 17 ( 10 unt; 0 nHn; 17 RR)
% Number of literals : 29 ( 0 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_Comb_Odiamond(A,B)
| ~ c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_Pair(C,E,B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B))
| c_in(c_Pair(D,c_Comb_Odiamond__strip__lemmaE__1(A,E,D,B),B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B)) ),
file('COL121-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_Comb_Odiamond(A,B)
| ~ c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_Pair(C,E,B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B))
| c_in(c_Pair(E,c_Comb_Odiamond__strip__lemmaE__1(A,E,D,B),B,B),A,tc_prod(B,B)) ),
file('COL121-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(A,B,tc_prod(C,C))
| c_in(A,c_Transitive__Closure_Ortrancl(B,C),tc_prod(C,C)) ),
file('COL121-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(c_Pair(A,B,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C))
| ~ c_in(c_Pair(E,A,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C))
| c_in(c_Pair(E,B,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C)) ),
file('COL121-2.p',unknown),
[] ).
cnf(5,axiom,
( c_in(c_Pair(v_ya,v_x(A),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('COL121-2.p',unknown),
[] ).
cnf(6,axiom,
( c_in(c_Pair(A,v_x(A),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('COL121-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_in(c_Pair(v_xaa,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,A,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_Comb_Odiamond(v_r,t_a),
file('COL121-2.p',unknown),
[] ).
cnf(9,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(10,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(12,plain,
c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[10,6]),
[iquote('hyper,10,6')] ).
cnf(13,plain,
c_in(c_Pair(v_ya,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[10,5]),
[iquote('hyper,10,5')] ).
cnf(21,plain,
c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[13,2,8,9]),
[iquote('hyper,13,2,8,9')] ).
cnf(22,plain,
c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[13,1,8,9]),
[iquote('hyper,13,1,8,9')] ).
cnf(40,plain,
c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[21,3]),
[iquote('hyper,21,3')] ).
cnf(101,plain,
c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[40,4,12]),
[iquote('hyper,40,4,12')] ).
cnf(108,plain,
$false,
inference(hyper,[status(thm)],[101,7,22]),
[iquote('hyper,101,7,22')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL121-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n017.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 : 300
% 0.12/0.34 % DateTime : Wed Jul 27 01:49:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.72/1.93 ----- Otter 3.3f, August 2004 -----
% 1.72/1.93 The process was started by sandbox on n017.cluster.edu,
% 1.72/1.93 Wed Jul 27 01:49:33 2022
% 1.72/1.93 The command was "./otter". The process ID is 20795.
% 1.72/1.93
% 1.72/1.93 set(prolog_style_variables).
% 1.72/1.93 set(auto).
% 1.72/1.93 dependent: set(auto1).
% 1.72/1.93 dependent: set(process_input).
% 1.72/1.93 dependent: clear(print_kept).
% 1.72/1.93 dependent: clear(print_new_demod).
% 1.72/1.93 dependent: clear(print_back_demod).
% 1.72/1.93 dependent: clear(print_back_sub).
% 1.72/1.93 dependent: set(control_memory).
% 1.72/1.93 dependent: assign(max_mem, 12000).
% 1.72/1.93 dependent: assign(pick_given_ratio, 4).
% 1.72/1.93 dependent: assign(stats_level, 1).
% 1.72/1.93 dependent: assign(max_seconds, 10800).
% 1.72/1.93 clear(print_given).
% 1.72/1.93
% 1.72/1.93 list(usable).
% 1.72/1.93 0 [] -c_Comb_Odiamond(V_r,T_a)| -c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))| -c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))|c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)).
% 1.72/1.93 0 [] -c_Comb_Odiamond(V_r,T_a)| -c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))| -c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))|c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)).
% 1.72/1.93 0 [] -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)).
% 1.72/1.93 0 [] -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)).
% 1.72/1.93 0 [] c_Comb_Odiamond(v_r,t_a).
% 1.72/1.93 0 [] c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.72/1.93 0 [] 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)).
% 1.72/1.93 0 [] c_in(c_Pair(v_ya,v_x(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_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)).
% 1.72/1.93 0 [] c_in(c_Pair(V_U,v_x(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_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)).
% 1.72/1.93 0 [] -c_in(c_Pair(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_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)).
% 1.72/1.93 end_of_list.
% 1.72/1.93
% 1.72/1.93 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.72/1.93
% 1.72/1.93 This is a Horn set without equality. The strategy will
% 1.72/1.93 be hyperresolution, with satellites in sos and nuclei
% 1.72/1.93 in usable.
% 1.72/1.93
% 1.72/1.93 dependent: set(hyper_res).
% 1.72/1.93 dependent: clear(order_hyper).
% 1.72/1.93
% 1.72/1.93 ------------> process usable:
% 1.72/1.93 ** KEPT (pick-wt=41): 1 [] -c_Comb_Odiamond(A,B)| -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))| -c_in(c_Pair(C,E,B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B))|c_in(c_Pair(D,c_Comb_Odiamond__strip__lemmaE__1(A,E,D,B),B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B)).
% 1.72/1.93 ** KEPT (pick-wt=39): 2 [] -c_Comb_Odiamond(A,B)| -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))| -c_in(c_Pair(C,E,B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B))|c_in(c_Pair(E,c_Comb_Odiamond__strip__lemmaE__1(A,E,D,B),B,B),A,tc_prod(B,B)).
% 1.72/1.93 ** KEPT (pick-wt=14): 3 [] -c_in(A,B,tc_prod(C,C))|c_in(A,c_Transitive__Closure_Ortrancl(B,C),tc_prod(C,C)).
% 1.72/1.93 ** KEPT (pick-wt=36): 4 [] -c_in(c_Pair(A,B,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C))| -c_in(c_Pair(E,A,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C))|c_in(c_Pair(E,B,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C)).
% 1.72/1.93 ** KEPT (pick-wt=25): 5 [] c_in(c_Pair(v_ya,v_x(A),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))| -c_in(c_Pair(v_y,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)).
% 1.72/1.93 ** KEPT (pick-wt=25): 6 [] c_in(c_Pair(A,v_x(A),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))| -c_in(c_Pair(v_y,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)).
% 1.72/1.93 ** KEPT (pick-wt=24): 7 [] -c_in(c_Pair(v_xaa,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))| -c_in(c_Pair(v_z,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)).
% 1.72/1.94
% 1.72/1.94 ------------> process sos:
% 1.72/1.94 ** KEPT (pick-wt=3): 8 [] c_Comb_Odiamond(v_r,t_a).
% 1.72/1.94 ** KEPT (pick-wt=10): 9 [] c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.72/1.94 ** KEPT (pick-wt=12): 10 [] 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)).
% 1.72/1.94
% 1.72/1.94 ======= end of input processing =======
% 1.72/1.94
% 1.72/1.94 =========== start of search ===========
% 1.72/1.94
% 1.72/1.94 -------- PROOF --------
% 1.72/1.94
% 1.72/1.94 -----> EMPTY CLAUSE at 0.01 sec ----> 108 [hyper,101,7,22] $F.
% 1.72/1.94
% 1.72/1.94 Length of proof is 6. Level of proof is 4.
% 1.72/1.94
% 1.72/1.94 ---------------- PROOF ----------------
% 1.72/1.94 % SZS status Unsatisfiable
% 1.72/1.94 % SZS output start Refutation
% See solution above
% 1.72/1.94 ------------ end of proof -------------
% 1.72/1.94
% 1.72/1.94
% 1.72/1.94 Search stopped by max_proofs option.
% 1.72/1.94
% 1.72/1.94
% 1.72/1.94 Search stopped by max_proofs option.
% 1.72/1.94
% 1.72/1.94 ============ end of search ============
% 1.72/1.94
% 1.72/1.94 -------------- statistics -------------
% 1.72/1.94 clauses given 48
% 1.72/1.94 clauses generated 116
% 1.72/1.94 clauses kept 107
% 1.72/1.94 clauses forward subsumed 18
% 1.72/1.94 clauses back subsumed 0
% 1.72/1.94 Kbytes malloced 976
% 1.72/1.94
% 1.72/1.94 ----------- times (seconds) -----------
% 1.72/1.94 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.72/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.94
% 1.72/1.94 That finishes the proof of the theorem.
% 1.72/1.94
% 1.72/1.94 Process 20795 finished Wed Jul 27 01:49:34 2022
% 1.72/1.94 Otter interrupted
% 1.72/1.94 PROOF FOUND
%------------------------------------------------------------------------------