%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP685-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 12:57:39 EDT 2022
% Result : Unsatisfiable 1.97s 2.12s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 5 RR)
% Number of literals : 32 ( 31 equ; 4 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; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
rd(mult(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
file('GRP685-11.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP685-11.p',unknown),
[] ).
cnf(4,axiom,
ld(A,mult(A,A)) = A,
file('GRP685-11.p',unknown),
[] ).
cnf(5,axiom,
rd(mult(A,A),A) = A,
file('GRP685-11.p',unknown),
[] ).
cnf(8,axiom,
mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('GRP685-11.p',unknown),
[] ).
cnf(9,axiom,
mult(rd(A,B),B) = rd(mult(A,B),B),
file('GRP685-11.p',unknown),
[] ).
cnf(11,plain,
rd(mult(A,B),B) = mult(rd(A,B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(12,axiom,
ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
file('GRP685-11.p',unknown),
[] ).
cnf(13,axiom,
rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('GRP685-11.p',unknown),
[] ).
cnf(14,plain,
mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13]),11,11]),
[iquote('copy,13,demod,11,11')] ).
cnf(16,axiom,
ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
file('GRP685-11.p',unknown),
[] ).
cnf(18,plain,
mult(rd(rd(A,A),B),B) = ld(A,mult(A,ld(B,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16]),11])]),
[iquote('copy,16,demod,11,flip.1')] ).
cnf(19,plain,
mult(rd(A,A),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[5]),11]),
[iquote('back_demod,5,demod,11')] ).
cnf(21,plain,
mult(rd(x6,rd(x7,x8)),rd(x7,x8)) != mult(rd(x6,x8),x8),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),11,11]),
[iquote('back_demod,1,demod,11,11')] ).
cnf(26,plain,
rd(A,A) = ld(A,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,19]),18,8,4]),
[iquote('para_into,10.1.1.1,19.1.1,demod,18,8,4')] ).
cnf(27,plain,
rd(ld(A,mult(A,B)),ld(A,B)) = mult(rd(A,ld(A,B)),ld(A,B)),
inference(para_into,[status(thm),theory(equality)],[11,8]),
[iquote('para_into,10.1.1.1,7.1.1')] ).
cnf(30,plain,
mult(ld(A,A),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),26]),
[iquote('back_demod,19,demod,26')] ).
cnf(31,plain,
mult(rd(ld(A,A),B),B) = ld(A,mult(A,ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),26]),
[iquote('back_demod,17,demod,26')] ).
cnf(35,plain,
mult(ld(A,mult(A,B)),C) = ld(A,mult(A,mult(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,4]),4])]),
[iquote('para_into,12.1.1.1,3.1.1,demod,4,flip.1')] ).
cnf(48,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(ld(A,A),mult(rd(A,C),C)),
inference(para_into,[status(thm),theory(equality)],[14,30]),
[iquote('para_into,14.1.1.1.1,29.1.1')] ).
cnf(56,plain,
mult(mult(ld(A,A),mult(rd(A,B),B)),rd(C,B)) = mult(A,mult(rd(rd(C,B),B),B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,11]),48]),
[iquote('para_into,14.1.1.1,10.1.1,demod,48')] ).
cnf(57,plain,
mult(ld(x6,x6),mult(rd(x6,x8),x8)) != mult(rd(x6,x8),x8),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),48]),
[iquote('back_demod,21,demod,48')] ).
cnf(78,plain,
ld(A,mult(A,mult(A,B))) = mult(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,4])]),
[iquote('para_into,34.1.1.1,3.1.1,flip.1')] ).
cnf(103,plain,
mult(rd(A,ld(A,A)),ld(A,A)) = rd(A,ld(A,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,4])]),
[iquote('para_into,27.1.1.1,3.1.1,flip.1')] ).
cnf(230,plain,
mult(rd(A,ld(B,B)),ld(B,B)) = mult(ld(A,A),mult(rd(A,B),B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,26]),26]),
[iquote('para_into,47.1.1.1.2,25.1.1,demod,26')] ).
cnf(241,plain,
rd(A,ld(A,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[103]),230,26,30,30])]),
[iquote('back_demod,103,demod,230,26,30,30,flip.1')] ).
cnf(260,plain,
mult(ld(A,A),mult(ld(A,A),mult(rd(A,B),B))) = mult(rd(A,B),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[241,48]),241,230])]),
[iquote('para_from,240.1.1,47.1.1.2,demod,241,230,flip.1')] ).
cnf(280,plain,
mult(mult(rd(A,B),B),B) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[56,241]),230,260,241,241,8,4]),
[iquote('para_into,56.1.1.2,240.1.1,demod,230,260,241,241,8,4')] ).
cnf(309,plain,
mult(ld(A,A),B) = ld(A,mult(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[280,31]),35,30])]),
[iquote('para_into,280.1.1.1,31.1.1,demod,35,30,flip.1')] ).
cnf(311,plain,
ld(A,mult(A,mult(rd(A,B),B))) = mult(rd(A,B),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[260]),309,309,8,78]),
[iquote('back_demod,259,demod,309,309,8,78')] ).
cnf(320,plain,
mult(rd(x6,x8),x8) != mult(rd(x6,x8),x8),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),309,311]),
[iquote('back_demod,57,demod,309,311')] ).
cnf(321,plain,
$false,
inference(binary,[status(thm)],[320,2]),
[iquote('binary,320.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP685-11 : TPTP v8.1.0. Released v8.1.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:28:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.97/2.12 ----- Otter 3.3f, August 2004 -----
% 1.97/2.12 The process was started by sandbox on n011.cluster.edu,
% 1.97/2.12 Wed Jul 27 05:28:40 2022
% 1.97/2.12 The command was "./otter". The process ID is 6790.
% 1.97/2.12
% 1.97/2.12 set(prolog_style_variables).
% 1.97/2.12 set(auto).
% 1.97/2.12 dependent: set(auto1).
% 1.97/2.12 dependent: set(process_input).
% 1.97/2.12 dependent: clear(print_kept).
% 1.97/2.12 dependent: clear(print_new_demod).
% 1.97/2.12 dependent: clear(print_back_demod).
% 1.97/2.12 dependent: clear(print_back_sub).
% 1.97/2.12 dependent: set(control_memory).
% 1.97/2.12 dependent: assign(max_mem, 12000).
% 1.97/2.12 dependent: assign(pick_given_ratio, 4).
% 1.97/2.12 dependent: assign(stats_level, 1).
% 1.97/2.12 dependent: assign(max_seconds, 10800).
% 1.97/2.12 clear(print_given).
% 1.97/2.12
% 1.97/2.12 list(usable).
% 1.97/2.12 0 [] A=A.
% 1.97/2.12 0 [] ld(A,mult(A,A))=A.
% 1.97/2.12 0 [] rd(mult(A,A),A)=A.
% 1.97/2.12 0 [] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.97/2.12 0 [] mult(rd(A,B),B)=rd(mult(A,B),B).
% 1.97/2.12 0 [] ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D).
% 1.97/2.12 0 [] rd(mult(mult(A,B),rd(C,D)),rd(C,D))=mult(A,rd(mult(B,D),D)).
% 1.97/2.12 0 [] ld(A,mult(A,ld(B,B)))=rd(mult(rd(A,A),B),B).
% 1.97/2.12 0 [] rd(mult(x6,rd(x7,x8)),rd(x7,x8))!=rd(mult(x6,x8),x8).
% 1.97/2.12 end_of_list.
% 1.97/2.12
% 1.97/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.97/2.12
% 1.97/2.12 All clauses are units, and equality is present; the
% 1.97/2.12 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.97/2.12
% 1.97/2.12 dependent: set(knuth_bendix).
% 1.97/2.12 dependent: set(anl_eq).
% 1.97/2.12 dependent: set(para_from).
% 1.97/2.12 dependent: set(para_into).
% 1.97/2.12 dependent: clear(para_from_right).
% 1.97/2.12 dependent: clear(para_into_right).
% 1.97/2.12 dependent: set(para_from_vars).
% 1.97/2.12 dependent: set(eq_units_both_ways).
% 1.97/2.12 dependent: set(dynamic_demod_all).
% 1.97/2.12 dependent: set(dynamic_demod).
% 1.97/2.12 dependent: set(order_eq).
% 1.97/2.12 dependent: set(back_demod).
% 1.97/2.12 dependent: set(lrpo).
% 1.97/2.12
% 1.97/2.12 ------------> process usable:
% 1.97/2.12 ** KEPT (pick-wt=15): 1 [] rd(mult(x6,rd(x7,x8)),rd(x7,x8))!=rd(mult(x6,x8),x8).
% 1.97/2.12
% 1.97/2.12 ------------> process sos:
% 1.97/2.12 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.97/2.12 ** KEPT (pick-wt=7): 3 [] ld(A,mult(A,A))=A.
% 1.97/2.12 ---> New Demodulator: 4 [new_demod,3] ld(A,mult(A,A))=A.
% 1.97/2.12 ** KEPT (pick-wt=7): 5 [] rd(mult(A,A),A)=A.
% 1.97/2.12 ---> New Demodulator: 6 [new_demod,5] rd(mult(A,A),A)=A.
% 1.97/2.12 ** KEPT (pick-wt=11): 7 [] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.97/2.12 ---> New Demodulator: 8 [new_demod,7] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.97/2.12 ** KEPT (pick-wt=11): 10 [copy,9,flip.1] rd(mult(A,B),B)=mult(rd(A,B),B).
% 1.97/2.12 ---> New Demodulator: 11 [new_demod,10] rd(mult(A,B),B)=mult(rd(A,B),B).
% 1.97/2.12 ** KEPT (pick-wt=19): 12 [] ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D).
% 1.97/2.12 ** KEPT (pick-wt=19): 14 [copy,13,demod,11,11] mult(rd(mult(A,B),rd(C,D)),rd(C,D))=mult(A,mult(rd(B,D),D)).
% 1.97/2.12 ---> New Demodulator: 15 [new_demod,14] mult(rd(mult(A,B),rd(C,D)),rd(C,D))=mult(A,mult(rd(B,D),D)).
% 1.97/2.12 ** KEPT (pick-wt=15): 17 [copy,16,demod,11,flip.1] mult(rd(rd(A,A),B),B)=ld(A,mult(A,ld(B,B))).
% 1.97/2.12 ---> New Demodulator: 18 [new_demod,17] mult(rd(rd(A,A),B),B)=ld(A,mult(A,ld(B,B))).
% 1.97/2.12 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.97/2.12 >>>> Starting back demodulation with 4.
% 1.97/2.12 >>>> Starting back demodulation with 6.
% 1.97/2.12 >>>> Starting back demodulation with 8.
% 1.97/2.12 >>>> Starting back demodulation with 11.
% 1.97/2.12 >> back demodulating 5 with 11.
% 1.97/2.12 >> back demodulating 1 with 11.
% 1.97/2.12 ** KEPT (pick-wt=19): 22 [copy,12,flip.1] mult(ld(A,mult(A,B)),C)=ld(ld(A,D),mult(ld(A,D),mult(B,C))).
% 1.97/2.12 >>>> Starting back demodulation with 15.
% 1.97/2.12 >>>> Starting back demodulation with 18.
% 1.97/2.12 >>>> Starting back demodulation with 20.
% 1.97/2.12 Following clause subsumed by 12 during input processing: 0 [copy,22,flip.1] ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D).
% 1.97/2.12
% 1.97/2.12 ======= end of input processing =======
% 1.97/2.12
% 1.97/2.12 =========== start of search ===========
% 1.97/2.12
% 1.97/2.12
% 1.97/2.12 Resetting weight limit to 15.
% 1.97/2.12
% 1.97/2.12
% 1.97/2.12 Resetting weight limit to 15.
% 1.97/2.12
% 1.97/2.12 sos_size=71
% 1.97/2.12
% 1.97/2.12 -------- PROOF --------
% 1.97/2.12
% 1.97/2.12 ----> UNIT CONFLICT at 0.02 sec ----> 321 [binary,320.1,2.1] $F.
% 1.97/2.12
% 1.97/2.12 Length of proof is 22. Level of proof is 12.
% 1.97/2.12
% 1.97/2.12 ---------------- PROOF ----------------
% 1.97/2.12 % SZS status Unsatisfiable
% 1.97/2.12 % SZS output start Refutation
% See solution above
% 1.97/2.12 ------------ end of proof -------------
% 1.97/2.12
% 1.97/2.12
% 1.97/2.12 Search stopped by max_proofs option.
% 1.97/2.12
% 1.97/2.12
% 1.97/2.12 Search stopped by max_proofs option.
% 1.97/2.12
% 1.97/2.12 ============ end of search ============
% 1.97/2.12
% 1.97/2.12 -------------- statistics -------------
% 1.97/2.12 clauses given 32
% 1.97/2.12 clauses generated 320
% 1.97/2.12 clauses kept 177
% 1.97/2.12 clauses forward subsumed 264
% 1.97/2.12 clauses back subsumed 2
% 1.97/2.12 Kbytes malloced 4882
% 1.97/2.12
% 1.97/2.12 ----------- times (seconds) -----------
% 1.97/2.12 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.97/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.12
% 1.97/2.12 That finishes the proof of the theorem.
% 1.97/2.12
% 1.97/2.12 Process 6790 finished Wed Jul 27 05:28:42 2022
% 1.97/2.12 Otter interrupted
% 1.97/2.12 PROOF FOUND
%------------------------------------------------------------------------------