%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU167+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:15:01 EDT 2022
% Result : Theorem 1.87s 2.07s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 6 RR)
% Number of literals : 14 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| subset(cartesian_product2(A,C),cartesian_product2(B,C)) ),
file('SEU167+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ subset(A,B)
| subset(cartesian_product2(C,A),cartesian_product2(C,B)) ),
file('SEU167+1.p',unknown),
[] ).
cnf(3,axiom,
~ subset(cartesian_product2(dollar_c4,dollar_c2),cartesian_product2(dollar_c3,dollar_c1)),
file('SEU167+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('SEU167+1.p',unknown),
[] ).
cnf(6,axiom,
subset(dollar_c4,dollar_c3),
file('SEU167+1.p',unknown),
[] ).
cnf(7,axiom,
subset(dollar_c2,dollar_c1),
file('SEU167+1.p',unknown),
[] ).
cnf(9,plain,
subset(cartesian_product2(dollar_c4,A),cartesian_product2(dollar_c3,A)),
inference(hyper,[status(thm)],[6,1]),
[iquote('hyper,6,1')] ).
cnf(10,plain,
subset(cartesian_product2(A,dollar_c2),cartesian_product2(A,dollar_c1)),
inference(hyper,[status(thm)],[7,2]),
[iquote('hyper,7,2')] ).
cnf(17,plain,
subset(cartesian_product2(dollar_c4,dollar_c2),cartesian_product2(dollar_c3,dollar_c1)),
inference(hyper,[status(thm)],[10,4,9]),
[iquote('hyper,10,4,9')] ).
cnf(18,plain,
$false,
inference(binary,[status(thm)],[17,3]),
[iquote('binary,17.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU167+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.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 07:26:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.87/2.07 ----- Otter 3.3f, August 2004 -----
% 1.87/2.07 The process was started by sandbox2 on n013.cluster.edu,
% 1.87/2.07 Wed Jul 27 07:26:15 2022
% 1.87/2.07 The command was "./otter". The process ID is 7580.
% 1.87/2.07
% 1.87/2.07 set(prolog_style_variables).
% 1.87/2.07 set(auto).
% 1.87/2.07 dependent: set(auto1).
% 1.87/2.07 dependent: set(process_input).
% 1.87/2.07 dependent: clear(print_kept).
% 1.87/2.07 dependent: clear(print_new_demod).
% 1.87/2.07 dependent: clear(print_back_demod).
% 1.87/2.07 dependent: clear(print_back_sub).
% 1.87/2.07 dependent: set(control_memory).
% 1.87/2.07 dependent: assign(max_mem, 12000).
% 1.87/2.07 dependent: assign(pick_given_ratio, 4).
% 1.87/2.07 dependent: assign(stats_level, 1).
% 1.87/2.07 dependent: assign(max_seconds, 10800).
% 1.87/2.07 clear(print_given).
% 1.87/2.07
% 1.87/2.07 formula_list(usable).
% 1.87/2.07 $T.
% 1.87/2.07 all A B subset(A,A).
% 1.87/2.07 all A B C (subset(A,B)->subset(cartesian_product2(A,C),cartesian_product2(B,C))&subset(cartesian_product2(C,A),cartesian_product2(C,B))).
% 1.87/2.07 -(all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D)))).
% 1.87/2.07 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.87/2.07 end_of_list.
% 1.87/2.07
% 1.87/2.07 -------> usable clausifies to:
% 1.87/2.07
% 1.87/2.07 list(usable).
% 1.87/2.07 0 [] $T.
% 1.87/2.07 0 [] subset(A,A).
% 1.87/2.07 0 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 1.87/2.07 0 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 1.87/2.07 0 [] subset($c4,$c3).
% 1.87/2.07 0 [] subset($c2,$c1).
% 1.87/2.07 0 [] -subset(cartesian_product2($c4,$c2),cartesian_product2($c3,$c1)).
% 1.87/2.07 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.87/2.07 end_of_list.
% 1.87/2.07
% 1.87/2.07 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.87/2.07
% 1.87/2.07 This is a Horn set without equality. The strategy will
% 1.87/2.07 be hyperresolution, with satellites in sos and nuclei
% 1.87/2.07 in usable.
% 1.87/2.07
% 1.87/2.07 dependent: set(hyper_res).
% 1.87/2.07 dependent: clear(order_hyper).
% 1.87/2.07
% 1.87/2.07 ------------> process usable:
% 1.87/2.07 ** KEPT (pick-wt=10): 1 [] -subset(A,B)|subset(cartesian_product2(A,C),cartesian_product2(B,C)).
% 1.87/2.07 ** KEPT (pick-wt=10): 2 [] -subset(A,B)|subset(cartesian_product2(C,A),cartesian_product2(C,B)).
% 1.87/2.07 ** KEPT (pick-wt=7): 3 [] -subset(cartesian_product2($c4,$c2),cartesian_product2($c3,$c1)).
% 1.87/2.07 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.87/2.07
% 1.87/2.07 ------------> process sos:
% 1.87/2.07 ** KEPT (pick-wt=3): 5 [] subset(A,A).
% 1.87/2.07 ** KEPT (pick-wt=3): 6 [] subset($c4,$c3).
% 1.87/2.07 ** KEPT (pick-wt=3): 7 [] subset($c2,$c1).
% 1.87/2.07
% 1.87/2.07 ======= end of input processing =======
% 1.87/2.07
% 1.87/2.07 =========== start of search ===========
% 1.87/2.07
% 1.87/2.07 -------- PROOF --------
% 1.87/2.07
% 1.87/2.07 ----> UNIT CONFLICT at 0.00 sec ----> 18 [binary,17.1,3.1] $F.
% 1.87/2.07
% 1.87/2.07 Length of proof is 3. Level of proof is 2.
% 1.87/2.07
% 1.87/2.07 ---------------- PROOF ----------------
% 1.87/2.07 % SZS status Theorem
% 1.87/2.07 % SZS output start Refutation
% See solution above
% 1.87/2.07 ------------ end of proof -------------
% 1.87/2.07
% 1.87/2.07
% 1.87/2.07 Search stopped by max_proofs option.
% 1.87/2.07
% 1.87/2.07
% 1.87/2.07 Search stopped by max_proofs option.
% 1.87/2.07
% 1.87/2.07 ============ end of search ============
% 1.87/2.07
% 1.87/2.07 -------------- statistics -------------
% 1.87/2.07 clauses given 6
% 1.87/2.07 clauses generated 23
% 1.87/2.07 clauses kept 17
% 1.87/2.07 clauses forward subsumed 13
% 1.87/2.07 clauses back subsumed 0
% 1.87/2.07 Kbytes malloced 976
% 1.87/2.07
% 1.87/2.07 ----------- times (seconds) -----------
% 1.87/2.07 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.07 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.87/2.07
% 1.87/2.07 That finishes the proof of the theorem.
% 1.87/2.07
% 1.87/2.07 Process 7580 finished Wed Jul 27 07:26:16 2022
% 1.87/2.07 Otter interrupted
% 1.87/2.07 PROOF FOUND
%------------------------------------------------------------------------------