TSTP Solution File: SET968+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:14:36 EDT 2022
% Result : Theorem 1.73s 1.95s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 9 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
cartesian_product2(set_union2(dollar_c6,dollar_c5),set_union2(dollar_c4,dollar_c3)) != set_union2(set_union2(set_union2(cartesian_product2(dollar_c6,dollar_c4),cartesian_product2(dollar_c6,dollar_c3)),cartesian_product2(dollar_c5,dollar_c4)),cartesian_product2(dollar_c5,dollar_c3)),
file('SET968+1.p',unknown),
[] ).
cnf(5,plain,
set_union2(set_union2(set_union2(cartesian_product2(dollar_c6,dollar_c4),cartesian_product2(dollar_c6,dollar_c3)),cartesian_product2(dollar_c5,dollar_c4)),cartesian_product2(dollar_c5,dollar_c3)) != cartesian_product2(set_union2(dollar_c6,dollar_c5),set_union2(dollar_c4,dollar_c3)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(6,axiom,
A = A,
file('SET968+1.p',unknown),
[] ).
cnf(11,axiom,
cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)),
file('SET968+1.p',unknown),
[] ).
cnf(13,plain,
set_union2(cartesian_product2(A,B),cartesian_product2(C,B)) = cartesian_product2(set_union2(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,axiom,
cartesian_product2(A,set_union2(B,C)) = set_union2(cartesian_product2(A,B),cartesian_product2(A,C)),
file('SET968+1.p',unknown),
[] ).
cnf(16,plain,
set_union2(cartesian_product2(A,B),cartesian_product2(A,C)) = cartesian_product2(A,set_union2(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,flip.1')] ).
cnf(18,axiom,
set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
file('SET968+1.p',unknown),
[] ).
cnf(19,plain,
cartesian_product2(set_union2(dollar_c6,dollar_c5),set_union2(dollar_c4,dollar_c3)) != cartesian_product2(set_union2(dollar_c6,dollar_c5),set_union2(dollar_c4,dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[5]),16,18,16,13]),
[iquote('back_demod,5,demod,16,18,16,13')] ).
cnf(20,plain,
$false,
inference(binary,[status(thm)],[19,6]),
[iquote('binary,19.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.19/0.34 % Computer : n003.cluster.edu
% 0.19/0.34 % Model : x86_64 x86_64
% 0.19/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.34 % Memory : 8042.1875MB
% 0.19/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Wed Jul 27 10:50:11 EDT 2022
% 0.19/0.34 % CPUTime :
% 1.73/1.95 ----- Otter 3.3f, August 2004 -----
% 1.73/1.95 The process was started by sandbox2 on n003.cluster.edu,
% 1.73/1.95 Wed Jul 27 10:50:11 2022
% 1.73/1.95 The command was "./otter". The process ID is 5788.
% 1.73/1.95
% 1.73/1.95 set(prolog_style_variables).
% 1.73/1.95 set(auto).
% 1.73/1.95 dependent: set(auto1).
% 1.73/1.95 dependent: set(process_input).
% 1.73/1.95 dependent: clear(print_kept).
% 1.73/1.95 dependent: clear(print_new_demod).
% 1.73/1.95 dependent: clear(print_back_demod).
% 1.73/1.95 dependent: clear(print_back_sub).
% 1.73/1.95 dependent: set(control_memory).
% 1.73/1.95 dependent: assign(max_mem, 12000).
% 1.73/1.95 dependent: assign(pick_given_ratio, 4).
% 1.73/1.95 dependent: assign(stats_level, 1).
% 1.73/1.95 dependent: assign(max_seconds, 10800).
% 1.73/1.95 clear(print_given).
% 1.73/1.95
% 1.73/1.95 formula_list(usable).
% 1.73/1.95 all A (A=A).
% 1.73/1.95 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.73/1.95 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.73/1.95 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.73/1.95 all A B (set_union2(A,A)=A).
% 1.73/1.95 exists A empty(A).
% 1.73/1.95 exists A (-empty(A)).
% 1.73/1.95 all A B C (cartesian_product2(set_union2(A,B),C)=set_union2(cartesian_product2(A,C),cartesian_product2(B,C))&cartesian_product2(C,set_union2(A,B))=set_union2(cartesian_product2(C,A),cartesian_product2(C,B))).
% 1.73/1.95 -(all A B C D (cartesian_product2(set_union2(A,B),set_union2(C,D))=set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)))).
% 1.73/1.95 all A B C (set_union2(set_union2(A,B),C)=set_union2(A,set_union2(B,C))).
% 1.73/1.95 end_of_list.
% 1.73/1.95
% 1.73/1.95 -------> usable clausifies to:
% 1.73/1.95
% 1.73/1.95 list(usable).
% 1.73/1.95 0 [] A=A.
% 1.73/1.95 0 [] set_union2(A,B)=set_union2(B,A).
% 1.73/1.95 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.73/1.95 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.73/1.95 0 [] set_union2(A,A)=A.
% 1.73/1.95 0 [] empty($c1).
% 1.73/1.95 0 [] -empty($c2).
% 1.73/1.95 0 [] cartesian_product2(set_union2(A,B),C)=set_union2(cartesian_product2(A,C),cartesian_product2(B,C)).
% 1.73/1.95 0 [] cartesian_product2(C,set_union2(A,B))=set_union2(cartesian_product2(C,A),cartesian_product2(C,B)).
% 1.73/1.95 0 [] cartesian_product2(set_union2($c6,$c5),set_union2($c4,$c3))!=set_union2(set_union2(set_union2(cartesian_product2($c6,$c4),cartesian_product2($c6,$c3)),cartesian_product2($c5,$c4)),cartesian_product2($c5,$c3)).
% 1.73/1.95 0 [] set_union2(set_union2(A,B),C)=set_union2(A,set_union2(B,C)).
% 1.73/1.95 end_of_list.
% 1.73/1.95
% 1.73/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.73/1.95
% 1.73/1.95 This is a Horn set with equality. The strategy will be
% 1.73/1.95 Knuth-Bendix and hyper_res, with positive clauses in
% 1.73/1.95 sos and nonpositive clauses in usable.
% 1.73/1.95
% 1.73/1.95 dependent: set(knuth_bendix).
% 1.73/1.95 dependent: set(anl_eq).
% 1.73/1.95 dependent: set(para_from).
% 1.73/1.95 dependent: set(para_into).
% 1.73/1.95 dependent: clear(para_from_right).
% 1.73/1.95 dependent: clear(para_into_right).
% 1.73/1.95 dependent: set(para_from_vars).
% 1.73/1.95 dependent: set(eq_units_both_ways).
% 1.73/1.95 dependent: set(dynamic_demod_all).
% 1.73/1.95 dependent: set(dynamic_demod).
% 1.73/1.95 dependent: set(order_eq).
% 1.73/1.95 dependent: set(back_demod).
% 1.73/1.95 dependent: set(lrpo).
% 1.73/1.95 dependent: set(hyper_res).
% 1.73/1.95 dependent: clear(order_hyper).
% 1.73/1.95
% 1.73/1.95 ------------> process usable:
% 1.73/1.95 ** KEPT (pick-wt=6): 1 [] empty(A)| -empty(set_union2(A,B)).
% 1.73/1.95 ** KEPT (pick-wt=6): 2 [] empty(A)| -empty(set_union2(B,A)).
% 1.73/1.95 ** KEPT (pick-wt=2): 3 [] -empty($c2).
% 1.73/1.95 ** KEPT (pick-wt=23): 5 [copy,4,flip.1] set_union2(set_union2(set_union2(cartesian_product2($c6,$c4),cartesian_product2($c6,$c3)),cartesian_product2($c5,$c4)),cartesian_product2($c5,$c3))!=cartesian_product2(set_union2($c6,$c5),set_union2($c4,$c3)).
% 1.73/1.95
% 1.73/1.95 ------------> process sos:
% 1.73/1.95 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.73/1.95 ** KEPT (pick-wt=7): 7 [] set_union2(A,B)=set_union2(B,A).
% 1.73/1.95 ** KEPT (pick-wt=5): 8 [] set_union2(A,A)=A.
% 1.73/1.95 ---> New Demodulator: 9 [new_demod,8] set_union2(A,A)=A.
% 1.73/1.95 ** KEPT (pick-wt=2): 10 [] empty($c1).
% 1.73/1.95 ** KEPT (pick-wt=13): 12 [copy,11,flip.1] set_union2(cartesian_product2(A,B),cartesian_product2(C,B))=cartesian_product2(set_union2(A,C),B).
% 1.73/1.95 ---> New Demodulator: 13 [new_demod,12] set_union2(cartesian_product2(A,B),cartesian_product2(C,B))=cartesian_product2(set_union2(A,C),B).
% 1.73/1.95 ** KEPT (pick-wt=13): 15 [copy,14,flip.1] set_union2(cartesian_product2(A,B),cartesian_product2(A,C))=cartesian_product2(A,set_union2(B,C)).
% 1.73/1.95 ---> New Demodulator: 16 [new_demod,15] set_union2(cartesian_product2(A,B),cartesian_product2(A,C))=cartesian_product2(A,set_union2(B,C)).
% 1.73/1.95 ** KEPT (pick-wt=11
% 1.73/1.95 -------- PROOF --------
% 1.73/1.95 ): 17 [] set_union2(set_union2(A,B),C)=set_union2(A,set_union2(B,C)).
% 1.73/1.95 ---> New Demodulator: 18 [new_demod,17] set_union2(set_union2(A,B),C)=set_union2(A,set_union2(B,C)).
% 1.73/1.95 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.73/1.95 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.73/1.95 >>>> Starting back demodulation with 9.
% 1.73/1.95 >>>> Starting back demodulation with 13.
% 1.73/1.95 >>>> Starting back demodulation with 16.
% 1.73/1.95 >> back demodulating 5 with 16.
% 1.73/1.95
% 1.73/1.95 ----> UNIT CONFLICT at 0.00 sec ----> 20 [binary,19.1,6.1] $F.
% 1.73/1.95
% 1.73/1.95 Length of proof is 4. Level of proof is 2.
% 1.73/1.95
% 1.73/1.95 ---------------- PROOF ----------------
% 1.73/1.95 % SZS status Theorem
% 1.73/1.95 % SZS output start Refutation
% See solution above
% 1.73/1.95 ------------ end of proof -------------
% 1.73/1.95
% 1.73/1.95
% 1.73/1.95 Search stopped by max_proofs option.
% 1.73/1.95
% 1.73/1.95
% 1.73/1.95 Search stopped by max_proofs option.
% 1.73/1.95
% 1.73/1.95 ============ end of search ============
% 1.73/1.95
% 1.73/1.95 -------------- statistics -------------
% 1.73/1.95 clauses given 0
% 1.73/1.95 clauses generated 0
% 1.73/1.95 clauses kept 12
% 1.73/1.95 clauses forward subsumed 2
% 1.73/1.95 clauses back subsumed 0
% 1.73/1.95 Kbytes malloced 976
% 1.73/1.95
% 1.73/1.95 ----------- times (seconds) -----------
% 1.73/1.95 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.73/1.95
% 1.73/1.95 That finishes the proof of the theorem.
% 1.73/1.95
% 1.73/1.95 Process 5788 finished Wed Jul 27 10:50:13 2022
% 1.73/1.95 Otter interrupted
% 1.73/1.95 PROOF FOUND
%------------------------------------------------------------------------------