%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG440-1 : TPTP v8.1.0. Released v5.4.0.
% 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 12:46:40 EDT 2022
% Result : Unsatisfiable 4.34s 4.55s
% Output : Refutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 34 ( 30 unt; 0 nHn; 21 RR)
% Number of literals : 46 ( 13 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ r(A,B,C)
| ~ r(D,E,F)
| ~ r(G,H,I)
| r(m(A,D,G),m(B,E,H),m(C,F,I)) ),
file('ALG440-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ r(A,B,C)
| ~ r(D,E,F)
| ~ r(G,H,I)
| r(u(A,D,G),u(B,E,H),u(C,F,I)) ),
file('ALG440-1.p',unknown),
[] ).
cnf(4,axiom,
~ r(a,a,a),
file('ALG440-1.p',unknown),
[] ).
cnf(7,axiom,
m(A,A,B) = B,
file('ALG440-1.p',unknown),
[] ).
cnf(9,axiom,
m(A,B,B) = A,
file('ALG440-1.p',unknown),
[] ).
cnf(11,axiom,
u(A,A,A) = A,
file('ALG440-1.p',unknown),
[] ).
cnf(14,axiom,
u(A,A,B) = u(A,B,A),
file('ALG440-1.p',unknown),
[] ).
cnf(15,axiom,
u(A,A,B) = u(B,A,A),
file('ALG440-1.p',unknown),
[] ).
cnf(16,axiom,
v(A,B) = v(B,A),
file('ALG440-1.p',unknown),
[] ).
cnf(17,axiom,
u(A,A,B) = v(A,B),
file('ALG440-1.p',unknown),
[] ).
cnf(19,plain,
v(A,B) = u(A,A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(20,axiom,
r(a,a,b),
file('ALG440-1.p',unknown),
[] ).
cnf(21,axiom,
r(a,b,a),
file('ALG440-1.p',unknown),
[] ).
cnf(22,axiom,
r(b,a,a),
file('ALG440-1.p',unknown),
[] ).
cnf(25,plain,
u(A,A,B) = u(B,B,A),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),19,19]),
[iquote('copy,16,flip.1,demod,19,19')] ).
cnf(26,plain,
r(a,u(b,a,b),u(a,b,a)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[21,2,21,20]),11]),
[iquote('hyper,21,2,21,20,demod,11')] ).
cnf(31,plain,
r(a,u(b,a,a),u(a,b,b)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[21,2,20,20]),11]),
[iquote('hyper,21,2,20,20,demod,11')] ).
cnf(36,plain,
r(u(a,b,b),u(b,a,a),a),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[22,2,21,22]),11]),
[iquote('hyper,22,2,21,22,demod,11')] ).
cnf(50,plain,
r(u(b,a,a),u(a,a,b),u(a,b,a)),
inference(hyper,[status(thm)],[22,2,20,21]),
[iquote('hyper,22,2,20,21')] ).
cnf(51,plain,
r(u(b,a,a),a,u(a,b,b)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[22,2,20,20]),11]),
[iquote('hyper,22,2,20,20,demod,11')] ).
cnf(59,plain,
( ~ r(A,B,C)
| ~ r(D,E,C)
| ~ r(F,G,H)
| r(m(A,D,F),m(B,E,G),H) ),
inference(para_from,[status(thm),theory(equality)],[7,1]),
[iquote('para_from,6.1.1,1.4.3')] ).
cnf(62,plain,
( ~ r(A,B,C)
| ~ r(D,E,F)
| ~ r(G,H,F)
| r(m(A,D,G),m(B,E,H),C) ),
inference(para_from,[status(thm),theory(equality)],[9,1]),
[iquote('para_from,8.1.1,1.4.3')] ).
cnf(373,plain,
u(A,B,B) = u(A,A,B),
inference(para_into,[status(thm),theory(equality)],[25,15]),
[iquote('para_into,25.1.1,15.1.1')] ).
cnf(374,plain,
u(A,B,A) = u(B,B,A),
inference(para_into,[status(thm),theory(equality)],[25,14]),
[iquote('para_into,25.1.1,14.1.1')] ).
cnf(375,plain,
u(A,A,B) = u(A,B,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[373])]),
[iquote('copy,373,flip.1')] ).
cnf(616,plain,
r(a,u(a,a,b),u(a,b,a)),
inference(para_into,[status(thm),theory(equality)],[26,374]),
[iquote('para_into,26.1.2,374.1.1')] ).
cnf(622,plain,
u(A,B,B) = u(B,A,A),
inference(para_into,[status(thm),theory(equality)],[375,15]),
[iquote('para_into,375.1.1,15.1.1')] ).
cnf(8995,plain,
r(u(b,a,a),b,a),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[616,59,50,21]),9,7]),
[iquote('hyper,616,59,50,21,demod,9,7')] ).
cnf(8996,plain,
r(u(b,a,a),a,b),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[616,59,50,20]),9,7]),
[iquote('hyper,616,59,50,20,demod,9,7')] ).
cnf(9140,plain,
r(u(a,b,b),b,a),
inference(para_into,[status(thm),theory(equality)],[8995,622]),
[iquote('para_into,8995.1.1,622.1.1')] ).
cnf(9148,plain,
r(a,u(b,a,a),b),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[8996,59,31,51]),9,9]),
[iquote('hyper,8996,59,31,51,demod,9,9')] ).
cnf(10618,plain,
r(a,b,b),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[9148,62,36,9140]),9,7]),
[iquote('hyper,9148,62,36,9140,demod,9,7')] ).
cnf(10901,plain,
r(a,a,a),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[10618,62,21,20]),7,7]),
[iquote('hyper,10618,62,21,20,demod,7,7')] ).
cnf(10902,plain,
$false,
inference(binary,[status(thm)],[10901,4]),
[iquote('binary,10901.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG440-1 : TPTP v8.1.0. Released v5.4.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 03:09:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.34/4.55 ----- Otter 3.3f, August 2004 -----
% 4.34/4.55 The process was started by sandbox2 on n017.cluster.edu,
% 4.34/4.55 Wed Jul 27 03:09:18 2022
% 4.34/4.55 The command was "./otter". The process ID is 4806.
% 4.34/4.55
% 4.34/4.55 set(prolog_style_variables).
% 4.34/4.55 set(auto).
% 4.34/4.55 dependent: set(auto1).
% 4.34/4.55 dependent: set(process_input).
% 4.34/4.55 dependent: clear(print_kept).
% 4.34/4.55 dependent: clear(print_new_demod).
% 4.34/4.55 dependent: clear(print_back_demod).
% 4.34/4.55 dependent: clear(print_back_sub).
% 4.34/4.55 dependent: set(control_memory).
% 4.34/4.55 dependent: assign(max_mem, 12000).
% 4.34/4.55 dependent: assign(pick_given_ratio, 4).
% 4.34/4.55 dependent: assign(stats_level, 1).
% 4.34/4.55 dependent: assign(max_seconds, 10800).
% 4.34/4.55 clear(print_given).
% 4.34/4.55
% 4.34/4.55 list(usable).
% 4.34/4.55 0 [] A=A.
% 4.34/4.55 0 [] m(A,A,B)=B.
% 4.34/4.55 0 [] m(A,B,B)=A.
% 4.34/4.55 0 [] u(A,A,A)=A.
% 4.34/4.55 0 [] v(A,A)=A.
% 4.34/4.55 0 [] u(A,A,B)=u(A,B,A).
% 4.34/4.55 0 [] u(A,A,B)=u(B,A,A).
% 4.34/4.55 0 [] v(A,B)=v(B,A).
% 4.34/4.55 0 [] u(A,A,B)=v(A,B).
% 4.34/4.55 0 [] -r(X0,X1,X2)| -r(X3,X4,X5)| -r(X6,X7,X8)|r(m(X0,X3,X6),m(X1,X4,X7),m(X2,X5,X8)).
% 4.34/4.55 0 [] -r(X0,X1,X2)| -r(X3,X4,X5)| -r(X6,X7,X8)|r(u(X0,X3,X6),u(X1,X4,X7),u(X2,X5,X8)).
% 4.34/4.55 0 [] -r(X0,X1,X2)| -r(X3,X4,X5)|r(v(X0,X3),v(X1,X4),v(X2,X5)).
% 4.34/4.55 0 [] r(a,a,b).
% 4.34/4.55 0 [] r(a,b,a).
% 4.34/4.55 0 [] r(b,a,a).
% 4.34/4.55 0 [] -r(a,a,a).
% 4.34/4.55 end_of_list.
% 4.34/4.55
% 4.34/4.55 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 4.34/4.55
% 4.34/4.55 This is a Horn set with equality. The strategy will be
% 4.34/4.55 Knuth-Bendix and hyper_res, with positive clauses in
% 4.34/4.55 sos and nonpositive clauses in usable.
% 4.34/4.55
% 4.34/4.55 dependent: set(knuth_bendix).
% 4.34/4.55 dependent: set(anl_eq).
% 4.34/4.55 dependent: set(para_from).
% 4.34/4.55 dependent: set(para_into).
% 4.34/4.55 dependent: clear(para_from_right).
% 4.34/4.55 dependent: clear(para_into_right).
% 4.34/4.55 dependent: set(para_from_vars).
% 4.34/4.55 dependent: set(eq_units_both_ways).
% 4.34/4.55 dependent: set(dynamic_demod_all).
% 4.34/4.55 dependent: set(dynamic_demod).
% 4.34/4.55 dependent: set(order_eq).
% 4.34/4.55 dependent: set(back_demod).
% 4.34/4.55 dependent: set(lrpo).
% 4.34/4.55 dependent: set(hyper_res).
% 4.34/4.55 dependent: clear(order_hyper).
% 4.34/4.55
% 4.34/4.55 ------------> process usable:
% 4.34/4.55 ** KEPT (pick-wt=25): 1 [] -r(A,B,C)| -r(D,E,F)| -r(G,H,I)|r(m(A,D,G),m(B,E,H),m(C,F,I)).
% 4.34/4.55 ** KEPT (pick-wt=25): 2 [] -r(A,B,C)| -r(D,E,F)| -r(G,H,I)|r(u(A,D,G),u(B,E,H),u(C,F,I)).
% 4.34/4.55 ** KEPT (pick-wt=18): 3 [] -r(A,B,C)| -r(D,E,F)|r(v(A,D),v(B,E),v(C,F)).
% 4.34/4.55 ** KEPT (pick-wt=4): 4 [] -r(a,a,a).
% 4.34/4.55
% 4.34/4.55 ------------> process sos:
% 4.34/4.55 ** KEPT (pick-wt=3): 5 [] A=A.
% 4.34/4.55 ** KEPT (pick-wt=6): 6 [] m(A,A,B)=B.
% 4.34/4.55 ---> New Demodulator: 7 [new_demod,6] m(A,A,B)=B.
% 4.34/4.55 ** KEPT (pick-wt=6): 8 [] m(A,B,B)=A.
% 4.34/4.55 ---> New Demodulator: 9 [new_demod,8] m(A,B,B)=A.
% 4.34/4.55 ** KEPT (pick-wt=6): 10 [] u(A,A,A)=A.
% 4.34/4.55 ---> New Demodulator: 11 [new_demod,10] u(A,A,A)=A.
% 4.34/4.55 ** KEPT (pick-wt=5): 12 [] v(A,A)=A.
% 4.34/4.55 ---> New Demodulator: 13 [new_demod,12] v(A,A)=A.
% 4.34/4.55 ** KEPT (pick-wt=9): 14 [] u(A,A,B)=u(A,B,A).
% 4.34/4.55 ** KEPT (pick-wt=9): 15 [] u(A,A,B)=u(B,A,A).
% 4.34/4.55 ** KEPT (pick-wt=7): 16 [] v(A,B)=v(B,A).
% 4.34/4.55 ** KEPT (pick-wt=8): 18 [copy,17,flip.1] v(A,B)=u(A,A,B).
% 4.34/4.55 ---> New Demodulator: 19 [new_demod,18] v(A,B)=u(A,A,B).
% 4.34/4.55 ** KEPT (pick-wt=4): 20 [] r(a,a,b).
% 4.34/4.55 ** KEPT (pick-wt=4): 21 [] r(a,b,a).
% 4.34/4.55 ** KEPT (pick-wt=4): 22 [] r(b,a,a).
% 4.34/4.55 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 4.34/4.55 >>>> Starting back demodulation with 7.
% 4.34/4.55 >>>> Starting back demodulation with 9.
% 4.34/4.55 >>>> Starting back demodulation with 11.
% 4.34/4.55 >>>> Starting back demodulation with 13.
% 4.34/4.55 ** KEPT (pick-wt=9): 23 [copy,14,flip.1] u(A,B,A)=u(A,A,B).
% 4.34/4.55 ** KEPT (pick-wt=9): 24 [copy,15,flip.1] u(A,B,B)=u(B,B,A).
% 4.34/4.55 ** KEPT (pick-wt=9): 25 [copy,16,flip.1,demod,19,19] u(A,A,B)=u(B,B,A).
% 4.34/4.55 >>>> Starting back demodulation with 19.
% 4.34/4.55 >> back demodulating 16 with 19.
% 4.34/4.55 >> back demodulating 12 with 19.
% 4.34/4.55 >> back demodulating 3 with 19.
% 4.34/4.55 Following clause subsumed by 14 during input processing: 0 [copy,23,flip.1] u(A,A,B)=u(A,B,A).
% 4.34/4.55 Following clause subsumed by 15 during input processing: 0 [copy,24,flip.1] u(A,A,B)=u(B,A,A).
% 4.34/4.55 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] u(A,A,B)=u(B,B,A).
% 4.34/4.55
% 4.34/4.55 ======= end of input processing =======
% 4.34/4.55
% 4.34/4.55 =========== start of search ===========
% 4.34/4.55
% 4.34/4.55
% 4.34/4.55 Resetting weight limit to 16.
% 4.34/4.55
% 4.34/4.55
% 4.34/4.55 Resetting weight limit to 16.
% 4.34/4.55
% 4.34/4.55 sos_size=7663
% 4.34/4.55
% 4.34/4.55
% 4.34/4.55 Resetting weight limit to 13.
% 4.34/4.55
% 4.34/4.55
% 4.34/4.55 Resetting weight limit to 13.
% 4.34/4.55
% 4.34/4.55 sos_size=8779
% 4.34/4.55
% 4.34/4.55 -------- PROOF --------
% 4.34/4.55
% 4.34/4.55 ----> UNIT CONFLICT at 2.65 sec ----> 10902 [binary,10901.1,4.1] $F.
% 4.34/4.55
% 4.34/4.55 Length of proof is 20. Level of proof is 8.
% 4.34/4.55
% 4.34/4.55 ---------------- PROOF ----------------
% 4.34/4.55 % SZS status Unsatisfiable
% 4.34/4.55 % SZS output start Refutation
% See solution above
% 4.34/4.55 ------------ end of proof -------------
% 4.34/4.55
% 4.34/4.55
% 4.34/4.55 Search stopped by max_proofs option.
% 4.34/4.55
% 4.34/4.55
% 4.34/4.55 Search stopped by max_proofs option.
% 4.34/4.55
% 4.34/4.55 ============ end of search ============
% 4.34/4.55
% 4.34/4.55 -------------- statistics -------------
% 4.34/4.55 clauses given 88
% 4.34/4.55 clauses generated 685125
% 4.34/4.55 clauses kept 10895
% 4.34/4.55 clauses forward subsumed 45391
% 4.34/4.55 clauses back subsumed 0
% 4.34/4.55 Kbytes malloced 6835
% 4.34/4.55
% 4.34/4.55 ----------- times (seconds) -----------
% 4.34/4.55 user CPU time 2.65 (0 hr, 0 min, 2 sec)
% 4.34/4.55 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 4.34/4.55 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 4.34/4.55
% 4.34/4.55 That finishes the proof of the theorem.
% 4.34/4.55
% 4.34/4.55 Process 4806 finished Wed Jul 27 03:09:22 2022
% 4.34/4.55 Otter interrupted
% 4.34/4.55 PROOF FOUND
%------------------------------------------------------------------------------