%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL123-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 12:48:18 EDT 2022
% Result : Unsatisfiable 1.68s 1.88s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 16 RR)
% Number of literals : 26 ( 0 equ; 11 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 : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(A,B,tc_prod(C,C))
| c_in(A,c_Transitive__Closure_Ortrancl(B,C),tc_prod(C,C)) ),
file('COL123-2.p',unknown),
[] ).
cnf(2,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('COL123-2.p',unknown),
[] ).
cnf(3,axiom,
( c_in(c_Pair(A,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_x,A,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_y,v_xaa(A),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,A,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_z,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xb,A,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(A,v_xa(B,A,C),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('COL123-2.p',unknown),
[] ).
cnf(7,axiom,
( c_in(c_Pair(A,v_xa(B,C,A),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('COL123-2.p',unknown),
[] ).
cnf(8,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(9,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(13,plain,
c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[9,4]),
[iquote('hyper,9,4')] ).
cnf(14,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(hyper,[status(thm)],[9,3]),
[iquote('hyper,9,3')] ).
cnf(18,plain,
c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[13,7,8]),
[iquote('hyper,13,7,8')] ).
cnf(20,plain,
c_in(c_Pair(v_z,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[13,6,8]),
[iquote('hyper,13,6,8')] ).
cnf(57,plain,
c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[18,1]),
[iquote('hyper,18,1')] ).
cnf(92,plain,
c_in(c_Pair(v_xb,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[57,2,14]),
[iquote('hyper,57,2,14')] ).
cnf(99,plain,
$false,
inference(hyper,[status(thm)],[92,5,20]),
[iquote('hyper,92,5,20')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL123-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n009.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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 02:20:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.88 ----- Otter 3.3f, August 2004 -----
% 1.68/1.88 The process was started by sandbox on n009.cluster.edu,
% 1.68/1.88 Wed Jul 27 02:20:21 2022
% 1.68/1.88 The command was "./otter". The process ID is 20341.
% 1.68/1.88
% 1.68/1.88 set(prolog_style_variables).
% 1.68/1.88 set(auto).
% 1.68/1.88 dependent: set(auto1).
% 1.68/1.88 dependent: set(process_input).
% 1.68/1.88 dependent: clear(print_kept).
% 1.68/1.88 dependent: clear(print_new_demod).
% 1.68/1.88 dependent: clear(print_back_demod).
% 1.68/1.88 dependent: clear(print_back_sub).
% 1.68/1.88 dependent: set(control_memory).
% 1.68/1.88 dependent: assign(max_mem, 12000).
% 1.68/1.88 dependent: assign(pick_given_ratio, 4).
% 1.68/1.88 dependent: assign(stats_level, 1).
% 1.68/1.88 dependent: assign(max_seconds, 10800).
% 1.68/1.88 clear(print_given).
% 1.68/1.88
% 1.68/1.88 list(usable).
% 1.68/1.88 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)).
% 1.68/1.88 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)).
% 1.68/1.88 0 [] c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.68/1.88 0 [] c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.68/1.88 0 [] 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)).
% 1.68/1.88 0 [] 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)).
% 1.68/1.88 0 [] -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)).
% 1.68/1.88 0 [] 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)).
% 1.68/1.88 0 [] 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)).
% 1.68/1.88 end_of_list.
% 1.68/1.88
% 1.68/1.88 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.68/1.88
% 1.68/1.88 This is a Horn set without equality. The strategy will
% 1.68/1.88 be hyperresolution, with satellites in sos and nuclei
% 1.68/1.88 in usable.
% 1.68/1.88
% 1.68/1.88 dependent: set(hyper_res).
% 1.68/1.88 dependent: clear(order_hyper).
% 1.68/1.88
% 1.68/1.88 ------------> process usable:
% 1.68/1.88 ** KEPT (pick-wt=14): 1 [] -c_in(A,B,tc_prod(C,C))|c_in(A,c_Transitive__Closure_Ortrancl(B,C),tc_prod(C,C)).
% 1.68/1.88 ** KEPT (pick-wt=36): 2 [] -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)).
% 1.68/1.88 ** KEPT (pick-wt=23): 3 [] c_in(c_Pair(A,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_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.68/1.88 ** KEPT (pick-wt=21): 4 [] c_in(c_Pair(v_y,v_xaa(A),t_a,t_a),v_r,tc_prod(t_a,t_a))| -c_in(c_Pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.68/1.88 ** KEPT (pick-wt=22): 5 [] -c_in(c_Pair(v_z,A,t_a,t_a),v_r,tc_prod(t_a,t_a))| -c_in(c_Pair(v_xb,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)).
% 1.68/1.88 ** KEPT (pick-wt=33): 6 [] c_in(c_Pair(A,v_xa(B,A,C),t_a,t_a),v_r,tc_prod(t_a,t_a))| -c_in(c_Pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))| -c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.68/1.88 ** KEPT (pick-wt=33): 7 [] c_in(c_Pair(A,v_xa(B,C,A),t_a,t_a),v_r,tc_prod(t_a,t_a))| -c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))| -c_in(c_Pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.68/1.88
% 1.68/1.88 ------------> process sos:
% 1.68/1.88 ** KEPT (pick-wt=10): 8 [] c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.68/1.88 ** KEPT (pick-wt=10): 9 [] c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.68/1.88
% 1.68/1.88 ======= end of input processing =======
% 1.68/1.88
% 1.68/1.88 =========== start of search ===========
% 1.68/1.88
% 1.68/1.88 -------- PROOF --------
% 1.68/1.88
% 1.68/1.88 -----> EMPTY CLAUSE at 0.00 sec ----> 99 [hyper,92,5,20] $F.
% 1.68/1.88
% 1.68/1.88 Length of proof is 6. Level of proof is 4.
% 1.68/1.88
% 1.68/1.88 ---------------- PROOF ----------------
% 1.68/1.88 % SZS status Unsatisfiable
% 1.68/1.88 % SZS output start Refutation
% See solution above
% 1.68/1.88 ------------ end of proof -------------
% 1.68/1.88
% 1.68/1.88
% 1.68/1.88 Search stopped by max_proofs option.
% 1.68/1.88
% 1.68/1.88
% 1.68/1.88 Search stopped by max_proofs option.
% 1.68/1.88
% 1.68/1.88 ============ end of search ============
% 1.68/1.88
% 1.68/1.88 -------------- statistics -------------
% 1.68/1.88 clauses given 37
% 1.68/1.88 clauses generated 131
% 1.68/1.88 clauses kept 98
% 1.68/1.88 clauses forward subsumed 41
% 1.68/1.88 clauses back subsumed 0
% 1.68/1.88 Kbytes malloced 976
% 1.68/1.88
% 1.68/1.88 ----------- times (seconds) -----------
% 1.68/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.88
% 1.68/1.88 That finishes the proof of the theorem.
% 1.68/1.88
% 1.68/1.88 Process 20341 finished Wed Jul 27 02:20:22 2022
% 1.68/1.88 Otter interrupted
% 1.68/1.88 PROOF FOUND
%------------------------------------------------------------------------------