TSTP Solution File: ALG236-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG236-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 12:46:25 EDT 2022
% Result : Unsatisfiable 2.41s 2.14s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 4 RR)
% Number of literals : 29 ( 28 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(mult(a,b),mult(c,mult(d,e))) != mult(a,mult(c,mult(mult(d,b),e))),
file('ALG236-1.p',unknown),
[] ).
cnf(2,plain,
mult(a,mult(c,mult(mult(d,b),e))) != mult(mult(a,b),mult(c,mult(d,e))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
mult(A,mult(B,mult(A,B))) = mult(A,B),
file('ALG236-1.p',unknown),
[] ).
cnf(6,axiom,
mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))),
file('ALG236-1.p',unknown),
[] ).
cnf(7,axiom,
mult(mult(A,mult(B,mult(C,B))),D) = mult(A,mult(D,mult(mult(C,B),D))),
file('ALG236-1.p',unknown),
[] ).
cnf(8,plain,
mult(A,mult(B,mult(mult(C,D),B))) = mult(mult(A,mult(D,mult(C,D))),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(13,plain,
mult(A,mult(B,mult(C,mult(D,E)))) = mult(C,mult(D,mult(A,mult(B,E)))),
inference(para_into,[status(thm),theory(equality)],[6,6]),
[iquote('para_into,6.1.1.2,6.1.1')] ).
cnf(15,plain,
mult(A,mult(B,mult(C,mult(B,A)))) = mult(C,mult(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,5])]),
[iquote('para_into,6.1.1.2,4.1.1,flip.1')] ).
cnf(22,plain,
mult(mult(d,b),mult(c,mult(a,e))) != mult(mult(a,b),mult(c,mult(d,e))),
inference(para_from,[status(thm),theory(equality)],[6,2]),
[iquote('para_from,6.1.1,2.1.1')] ).
cnf(49,plain,
mult(mult(A,B),mult(B,mult(A,B))) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,5]),5]),
[iquote('para_into,14.1.1.2.2,4.1.1,demod,5')] ).
cnf(69,plain,
mult(A,mult(B,mult(mult(A,C),B))) = mult(mult(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,5])]),
[iquote('para_into,7.1.1.1,4.1.1,flip.1')] ).
cnf(114,plain,
mult(mult(A,B),B) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,6]),69]),
[iquote('para_into,49.1.1,6.1.1,demod,69')] ).
cnf(135,plain,
mult(A,mult(B,mult(C,D))) = mult(C,mult(mult(B,mult(C,D)),mult(A,D))),
inference(para_from,[status(thm),theory(equality)],[114,6]),
[iquote('para_from,113.1.1,6.1.1.2')] ).
cnf(136,plain,
mult(A,mult(B,mult(C,D))) = mult(mult(C,D),mult(B,mult(A,D))),
inference(para_from,[status(thm),theory(equality)],[114,6]),
[iquote('para_from,113.1.1,6.1.1.2.2')] ).
cnf(139,plain,
mult(A,mult(B,mult(mult(mult(A,C),D),B))) = mult(mult(mult(A,C),D),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[69,69]),69]),
[iquote('para_into,68.1.1.2.2.1,68.1.1,demod,69')] ).
cnf(145,plain,
mult(A,mult(B,mult(C,mult(B,mult(A,D))))) = mult(C,mult(B,mult(A,D))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[69,15]),114,15]),
[iquote('para_into,68.1.1.2.2,14.1.1,demod,114,15')] ).
cnf(154,plain,
mult(mult(A,B),mult(C,mult(A,C))) = mult(mult(A,B),C),
inference(para_into,[status(thm),theory(equality)],[69,6]),
[iquote('para_into,68.1.1,6.1.1')] ).
cnf(244,plain,
mult(mult(mult(A,B),C),mult(D,mult(A,D))) = mult(mult(mult(A,B),C),D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[154,69]),69]),
[iquote('para_into,154.1.1.1,68.1.1,demod,69')] ).
cnf(263,plain,
mult(mult(mult(mult(A,B),C),B),D) = mult(mult(mult(A,B),C),D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[154,8]),244]),
[iquote('para_into,154.1.1,8.1.1,demod,244')] ).
cnf(280,plain,
mult(mult(mult(A,B),C),D) = mult(mult(A,B),mult(D,mult(mult(A,C),D))),
inference(para_from,[status(thm),theory(equality)],[154,7]),
[iquote('para_from,154.1.1,7.1.1.1')] ).
cnf(350,plain,
mult(mult(A,B),mult(C,mult(D,B))) = mult(A,mult(C,mult(D,B))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[136,6])]),
[iquote('para_into,136.1.1,6.1.1,flip.1')] ).
cnf(737,plain,
mult(mult(A,B),mult(C,mult(D,mult(mult(C,mult(D,E)),mult(A,E))))) = mult(mult(A,B),mult(C,mult(D,E))),
inference(para_from,[status(thm),theory(equality)],[13,154]),
[iquote('para_from,13.1.1,154.1.1.2')] ).
cnf(1748,plain,
mult(A,mult(mult(B,mult(A,C)),mult(D,C))) = mult(A,mult(B,mult(D,C))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[135,6])]),
[iquote('para_into,135.1.1,6.1.1,flip.1')] ).
cnf(1767,plain,
mult(mult(A,B),mult(C,mult(D,mult(C,mult(A,E))))) = mult(mult(A,B),mult(C,mult(D,E))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[737]),1748]),
[iquote('back_demod,737,demod,1748')] ).
cnf(2205,plain,
mult(mult(mult(A,B),C),mult(D,mult(A,mult(D,E)))) = mult(mult(mult(A,B),C),mult(D,E)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[139,13]),114]),
[iquote('para_into,139.1.1,13.1.1,demod,114')] ).
cnf(2400,plain,
mult(mult(mult(A,B),C),D) = mult(mult(mult(A,C),B),D),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[280,263]),350,69]),
[iquote('para_from,280.1.1,263.1.1.1,demod,350,69')] ).
cnf(2426,plain,
mult(mult(mult(A,B),C),B) = mult(mult(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2400,114])]),
[iquote('para_into,2400.1.1,113.1.1,flip.1')] ).
cnf(2459,plain,
mult(mult(A,B),mult(C,mult(D,E))) = mult(mult(D,B),mult(C,mult(A,E))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2426,145]),2205,2426,1767]),
[iquote('para_into,2425.1.1.1.1,145.1.1,demod,2205,2426,1767')] ).
cnf(2460,plain,
$false,
inference(binary,[status(thm)],[2459,22]),
[iquote('binary,2459.1,22.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG236-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 03:50:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.41/2.14 ----- Otter 3.3f, August 2004 -----
% 2.41/2.14 The process was started by sandbox2 on n008.cluster.edu,
% 2.41/2.14 Wed Jul 27 03:50:53 2022
% 2.41/2.14 The command was "./otter". The process ID is 4092.
% 2.41/2.14
% 2.41/2.14 set(prolog_style_variables).
% 2.41/2.14 set(auto).
% 2.41/2.14 dependent: set(auto1).
% 2.41/2.14 dependent: set(process_input).
% 2.41/2.14 dependent: clear(print_kept).
% 2.41/2.14 dependent: clear(print_new_demod).
% 2.41/2.14 dependent: clear(print_back_demod).
% 2.41/2.14 dependent: clear(print_back_sub).
% 2.41/2.14 dependent: set(control_memory).
% 2.41/2.14 dependent: assign(max_mem, 12000).
% 2.41/2.14 dependent: assign(pick_given_ratio, 4).
% 2.41/2.14 dependent: assign(stats_level, 1).
% 2.41/2.14 dependent: assign(max_seconds, 10800).
% 2.41/2.14 clear(print_given).
% 2.41/2.14
% 2.41/2.14 list(usable).
% 2.41/2.14 0 [] A=A.
% 2.41/2.14 0 [] mult(A,mult(B,mult(A,B)))=mult(A,B).
% 2.41/2.14 0 [] mult(A,mult(B,mult(C,D)))=mult(C,mult(B,mult(A,D))).
% 2.41/2.14 0 [] mult(mult(A,mult(B,mult(C,B))),D)=mult(A,mult(D,mult(mult(C,B),D))).
% 2.41/2.14 0 [] mult(mult(a,b),mult(c,mult(d,e)))!=mult(a,mult(c,mult(mult(d,b),e))).
% 2.41/2.14 end_of_list.
% 2.41/2.14
% 2.41/2.14 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.41/2.14
% 2.41/2.14 All clauses are units, and equality is present; the
% 2.41/2.14 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.41/2.14
% 2.41/2.14 dependent: set(knuth_bendix).
% 2.41/2.14 dependent: set(anl_eq).
% 2.41/2.14 dependent: set(para_from).
% 2.41/2.14 dependent: set(para_into).
% 2.41/2.14 dependent: clear(para_from_right).
% 2.41/2.14 dependent: clear(para_into_right).
% 2.41/2.14 dependent: set(para_from_vars).
% 2.41/2.14 dependent: set(eq_units_both_ways).
% 2.41/2.14 dependent: set(dynamic_demod_all).
% 2.41/2.14 dependent: set(dynamic_demod).
% 2.41/2.14 dependent: set(order_eq).
% 2.41/2.14 dependent: set(back_demod).
% 2.41/2.14 dependent: set(lrpo).
% 2.41/2.14
% 2.41/2.14 ------------> process usable:
% 2.41/2.14 ** KEPT (pick-wt=19): 2 [copy,1,flip.1] mult(a,mult(c,mult(mult(d,b),e)))!=mult(mult(a,b),mult(c,mult(d,e))).
% 2.41/2.14
% 2.41/2.14 ------------> process sos:
% 2.41/2.14 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.41/2.14 ** KEPT (pick-wt=11): 4 [] mult(A,mult(B,mult(A,B)))=mult(A,B).
% 2.41/2.14 ---> New Demodulator: 5 [new_demod,4] mult(A,mult(B,mult(A,B)))=mult(A,B).
% 2.41/2.14 ** KEPT (pick-wt=15): 6 [] mult(A,mult(B,mult(C,D)))=mult(C,mult(B,mult(A,D))).
% 2.41/2.14 ** KEPT (pick-wt=19): 7 [] mult(mult(A,mult(B,mult(C,B))),D)=mult(A,mult(D,mult(mult(C,B),D))).
% 2.41/2.14 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.41/2.14 >>>> Starting back demodulation with 5.
% 2.41/2.14 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] mult(A,mult(B,mult(C,D)))=mult(C,mult(B,mult(A,D))).
% 2.41/2.14 ** KEPT (pick-wt=19): 8 [copy,7,flip.1] mult(A,mult(B,mult(mult(C,D),B)))=mult(mult(A,mult(D,mult(C,D))),B).
% 2.41/2.14 Following clause subsumed by 7 during input processing: 0 [copy,8,flip.1] mult(mult(A,mult(B,mult(C,B))),D)=mult(A,mult(D,mult(mult(C,B),D))).
% 2.41/2.14
% 2.41/2.14 ======= end of input processing =======
% 2.41/2.14
% 2.41/2.14 =========== start of search ===========
% 2.41/2.14
% 2.41/2.14
% 2.41/2.14 Resetting weight limit to 23.
% 2.41/2.14
% 2.41/2.14
% 2.41/2.14 Resetting weight limit to 23.
% 2.41/2.14
% 2.41/2.14 sos_size=1522
% 2.41/2.14
% 2.41/2.14 -------- PROOF --------
% 2.41/2.14
% 2.41/2.14 ----> UNIT CONFLICT at 0.24 sec ----> 2460 [binary,2459.1,22.1] $F.
% 2.41/2.14
% 2.41/2.14 Length of proof is 24. Level of proof is 8.
% 2.41/2.14
% 2.41/2.14 ---------------- PROOF ----------------
% 2.41/2.14 % SZS status Unsatisfiable
% 2.41/2.14 % SZS output start Refutation
% See solution above
% 2.41/2.14 ------------ end of proof -------------
% 2.41/2.14
% 2.41/2.14
% 2.41/2.14 Search stopped by max_proofs option.
% 2.41/2.14
% 2.41/2.14
% 2.41/2.14 Search stopped by max_proofs option.
% 2.41/2.14
% 2.41/2.14 ============ end of search ============
% 2.41/2.14
% 2.41/2.14 -------------- statistics -------------
% 2.41/2.14 clauses given 49
% 2.41/2.14 clauses generated 6365
% 2.41/2.14 clauses kept 2014
% 2.41/2.14 clauses forward subsumed 4261
% 2.41/2.14 clauses back subsumed 20
% 2.41/2.14 Kbytes malloced 4882
% 2.41/2.14
% 2.41/2.14 ----------- times (seconds) -----------
% 2.41/2.14 user CPU time 0.24 (0 hr, 0 min, 0 sec)
% 2.41/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.41/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.41/2.14
% 2.41/2.14 That finishes the proof of the theorem.
% 2.41/2.14
% 2.41/2.14 Process 4092 finished Wed Jul 27 03:50:55 2022
% 2.41/2.14 Otter interrupted
% 2.41/2.14 PROOF FOUND
%------------------------------------------------------------------------------