%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG235-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 1.97s 2.13s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 3 RR)
% Number of literals : 14 ( 13 equ; 2 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))),
file('ALG235-1.p',unknown),
[] ).
cnf(4,axiom,
mult(A,mult(B,mult(A,B))) = mult(A,B),
file('ALG235-1.p',unknown),
[] ).
cnf(5,axiom,
mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))),
file('ALG235-1.p',unknown),
[] ).
cnf(6,axiom,
mult(mult(A,mult(B,mult(C,B))),D) = mult(A,mult(D,mult(mult(C,B),D))),
file('ALG235-1.p',unknown),
[] ).
cnf(8,plain,
mult(A,mult(mult(B,mult(A,B)),mult(A,B))) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4]),4]),
[iquote('para_into,3.1.1.2.2,3.1.1,demod,4')] ).
cnf(14,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)],[5,4])]),
[iquote('para_into,5.1.1.2,3.1.1,flip.1')] ).
cnf(21,plain,
mult(a,mult(c,mult(a,mult(b,mult(d,c))))) != mult(a,mult(b,mult(d,c))),
inference(para_from,[status(thm),theory(equality)],[5,1]),
[iquote('para_from,5.1.1,1.1.1.2')] ).
cnf(29,plain,
mult(A,mult(mult(B,mult(A,mult(mult(B,C),C))),mult(A,mult(B,C)))) = mult(A,mult(B,C)),
inference(para_into,[status(thm),theory(equality)],[8,5]),
[iquote('para_into,8.1.1.2.1,5.1.1')] ).
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)],[14,4]),4]),
[iquote('para_into,13.1.1.2.2,3.1.1,demod,4')] ).
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)],[6,4])]),
[iquote('para_into,6.1.1.1,3.1.1,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)],[49,5]),69]),
[iquote('para_into,49.1.1,5.1.1,demod,69')] ).
cnf(117,plain,
mult(A,mult(B,mult(A,mult(B,C)))) = mult(A,mult(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),114,114]),
[iquote('back_demod,29,demod,114,114')] ).
cnf(167,plain,
mult(A,mult(B,mult(A,mult(C,mult(D,B))))) = mult(A,mult(C,mult(D,B))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[117,14]),14]),
[iquote('para_into,117.1.1.2.2.2,13.1.1,demod,14')] ).
cnf(169,plain,
$false,
inference(binary,[status(thm)],[167,21]),
[iquote('binary,167.1,21.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG235-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n015.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 03:59:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.97/2.13 ----- Otter 3.3f, August 2004 -----
% 1.97/2.13 The process was started by sandbox on n015.cluster.edu,
% 1.97/2.13 Wed Jul 27 03:59:26 2022
% 1.97/2.13 The command was "./otter". The process ID is 4388.
% 1.97/2.13
% 1.97/2.13 set(prolog_style_variables).
% 1.97/2.13 set(auto).
% 1.97/2.13 dependent: set(auto1).
% 1.97/2.13 dependent: set(process_input).
% 1.97/2.13 dependent: clear(print_kept).
% 1.97/2.13 dependent: clear(print_new_demod).
% 1.97/2.13 dependent: clear(print_back_demod).
% 1.97/2.13 dependent: clear(print_back_sub).
% 1.97/2.13 dependent: set(control_memory).
% 1.97/2.13 dependent: assign(max_mem, 12000).
% 1.97/2.13 dependent: assign(pick_given_ratio, 4).
% 1.97/2.13 dependent: assign(stats_level, 1).
% 1.97/2.13 dependent: assign(max_seconds, 10800).
% 1.97/2.13 clear(print_given).
% 1.97/2.13
% 1.97/2.13 list(usable).
% 1.97/2.13 0 [] A=A.
% 1.97/2.13 0 [] mult(A,mult(B,mult(A,B)))=mult(A,B).
% 1.97/2.13 0 [] mult(A,mult(B,mult(C,D)))=mult(C,mult(B,mult(A,D))).
% 1.97/2.13 0 [] mult(mult(A,mult(B,mult(C,B))),D)=mult(A,mult(D,mult(mult(C,B),D))).
% 1.97/2.13 0 [] mult(a,mult(b,mult(a,mult(c,mult(d,c)))))!=mult(a,mult(b,mult(d,c))).
% 1.97/2.13 end_of_list.
% 1.97/2.13
% 1.97/2.13 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.97/2.13
% 1.97/2.13 All clauses are units, and equality is present; the
% 1.97/2.13 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.97/2.13
% 1.97/2.13 dependent: set(knuth_bendix).
% 1.97/2.13 dependent: set(anl_eq).
% 1.97/2.13 dependent: set(para_from).
% 1.97/2.13 dependent: set(para_into).
% 1.97/2.13 dependent: clear(para_from_right).
% 1.97/2.13 dependent: clear(para_into_right).
% 1.97/2.13 dependent: set(para_from_vars).
% 1.97/2.13 dependent: set(eq_units_both_ways).
% 1.97/2.13 dependent: set(dynamic_demod_all).
% 1.97/2.13 dependent: set(dynamic_demod).
% 1.97/2.13 dependent: set(order_eq).
% 1.97/2.13 dependent: set(back_demod).
% 1.97/2.13 dependent: set(lrpo).
% 1.97/2.13
% 1.97/2.13 ------------> process usable:
% 1.97/2.13 ** KEPT (pick-wt=19): 1 [] mult(a,mult(b,mult(a,mult(c,mult(d,c)))))!=mult(a,mult(b,mult(d,c))).
% 1.97/2.13
% 1.97/2.13 ------------> process sos:
% 1.97/2.13 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.97/2.13 ** KEPT (pick-wt=11): 3 [] mult(A,mult(B,mult(A,B)))=mult(A,B).
% 1.97/2.13 ---> New Demodulator: 4 [new_demod,3] mult(A,mult(B,mult(A,B)))=mult(A,B).
% 1.97/2.13 ** KEPT (pick-wt=15): 5 [] mult(A,mult(B,mult(C,D)))=mult(C,mult(B,mult(A,D))).
% 1.97/2.13 ** KEPT (pick-wt=19): 6 [] mult(mult(A,mult(B,mult(C,B))),D)=mult(A,mult(D,mult(mult(C,B),D))).
% 1.97/2.13 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.97/2.13 >>>> Starting back demodulation with 4.
% 1.97/2.13 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] mult(A,mult(B,mult(C,D)))=mult(C,mult(B,mult(A,D))).
% 1.97/2.13 ** KEPT (pick-wt=19): 7 [copy,6,flip.1] mult(A,mult(B,mult(mult(C,D),B)))=mult(mult(A,mult(D,mult(C,D))),B).
% 1.97/2.13 Following clause subsumed by 6 during input processing: 0 [copy,7,flip.1] mult(mult(A,mult(B,mult(C,B))),D)=mult(A,mult(D,mult(mult(C,B),D))).
% 1.97/2.13
% 1.97/2.13 ======= end of input processing =======
% 1.97/2.13
% 1.97/2.13 =========== start of search ===========
% 1.97/2.13
% 1.97/2.13 -------- PROOF --------
% 1.97/2.13
% 1.97/2.13 ----> UNIT CONFLICT at 0.01 sec ----> 169 [binary,167.1,21.1] $F.
% 1.97/2.13
% 1.97/2.13 Length of proof is 9. Level of proof is 5.
% 1.97/2.13
% 1.97/2.13 ---------------- PROOF ----------------
% 1.97/2.13 % SZS status Unsatisfiable
% 1.97/2.13 % SZS output start Refutation
% See solution above
% 1.97/2.13 ------------ end of proof -------------
% 1.97/2.13
% 1.97/2.13
% 1.97/2.13 Search stopped by max_proofs option.
% 1.97/2.13
% 1.97/2.13
% 1.97/2.13 Search stopped by max_proofs option.
% 1.97/2.13
% 1.97/2.13 ============ end of search ============
% 1.97/2.13
% 1.97/2.13 -------------- statistics -------------
% 1.97/2.13 clauses given 10
% 1.97/2.13 clauses generated 175
% 1.97/2.13 clauses kept 115
% 1.97/2.13 clauses forward subsumed 145
% 1.97/2.13 clauses back subsumed 0
% 1.97/2.13 Kbytes malloced 1953
% 1.97/2.13
% 1.97/2.13 ----------- times (seconds) -----------
% 1.97/2.13 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.97/2.13 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.13 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.13
% 1.97/2.13 That finishes the proof of the theorem.
% 1.97/2.13
% 1.97/2.13 Process 4388 finished Wed Jul 27 03:59:28 2022
% 1.97/2.13 Otter interrupted
% 1.97/2.13 PROOF FOUND
%------------------------------------------------------------------------------