%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 12:57:11 EDT 2022
% Result : Unsatisfiable 1.92s 2.10s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 6 RR)
% Number of literals : 28 ( 27 equ; 5 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP525-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
divide(A,divide(divide(A,B),divide(C,B))) = C,
file('GRP525-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP525-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP525-1.p',unknown),
[] ).
cnf(8,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,plain,
divide(divide(A,A),B) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(11,plain,
multiply(divide(divide(A,A),b1),b1) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[7,2]),
[iquote('para_from,7.1.1,2.1.1.1')] ).
cnf(12,plain,
multiply(inverse(a1),a1) != multiply(divide(divide(A,A),b1),b1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(13,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.1,9.1.1')] ).
cnf(37,plain,
divide(A,inverse(divide(B,A))) = B,
inference(para_into,[status(thm),theory(equality)],[4,9]),
[iquote('para_into,4.1.1.2,9.1.1')] ).
cnf(47,plain,
divide(inverse(divide(A,B)),inverse(A)) = B,
inference(para_into,[status(thm),theory(equality)],[37,37]),
[iquote('para_into,37.1.1.2.1,37.1.1')] ).
cnf(51,plain,
divide(divide(divide(A,B),divide(C,B)),inverse(C)) = A,
inference(para_into,[status(thm),theory(equality)],[37,4]),
[iquote('para_into,37.1.1.2.1,4.1.1')] ).
cnf(59,plain,
inverse(inverse(divide(A,divide(B,B)))) = A,
inference(para_into,[status(thm),theory(equality)],[37,9]),
[iquote('para_into,37.1.1,9.1.1')] ).
cnf(70,plain,
inverse(divide(A,B)) = divide(inverse(A),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,37])]),
[iquote('para_into,47.1.1.1.1,37.1.1,flip.1')] ).
cnf(85,plain,
inverse(inverse(A)) = A,
inference(para_into,[status(thm),theory(equality)],[47,13]),
[iquote('para_into,47.1.1,13.1.1')] ).
cnf(92,plain,
divide(A,divide(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),70,70,70,85,70,85,85]),
[iquote('back_demod,59,demod,70,70,70,85,70,85,85')] ).
cnf(109,plain,
divide(divide(A,A),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[85,7]),
[iquote('para_into,84.1.1,7.1.1')] ).
cnf(110,plain,
divide(A,divide(A,B)) = B,
inference(para_from,[status(thm),theory(equality)],[92,4]),
[iquote('para_from,92.1.1,4.1.1.2')] ).
cnf(115,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[110,4])]),
[iquote('para_into,110.1.1.2,4.1.1,flip.1')] ).
cnf(118,plain,
divide(divide(A,B),inverse(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[51]),115]),
[iquote('back_demod,51,demod,115')] ).
cnf(132,plain,
multiply(A,divide(divide(B,B),C)) = divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,110])]),
[iquote('para_into,8.1.1.2,110.1.1,flip.1')] ).
cnf(135,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[8,9]),
[iquote('para_into,8.1.1.2,9.1.1')] ).
cnf(142,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[135])]),
[iquote('copy,135,flip.1')] ).
cnf(149,plain,
divide(multiply(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,118]),70,70,109]),
[iquote('para_from,8.1.1,118.1.1.1,demod,70,70,109')] ).
cnf(159,plain,
multiply(divide(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[149,8]),132]),
[iquote('para_into,149.1.1,8.1.1,demod,132')] ).
cnf(160,plain,
multiply(inverse(a1),a1) != divide(A,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),159]),
[iquote('back_demod,12,demod,159')] ).
cnf(161,plain,
$false,
inference(binary,[status(thm)],[160,142]),
[iquote('binary,160.1,142.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n023.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 05:22:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.92/2.10 ----- Otter 3.3f, August 2004 -----
% 1.92/2.10 The process was started by sandbox2 on n023.cluster.edu,
% 1.92/2.10 Wed Jul 27 05:22:33 2022
% 1.92/2.10 The command was "./otter". The process ID is 6306.
% 1.92/2.10
% 1.92/2.10 set(prolog_style_variables).
% 1.92/2.10 set(auto).
% 1.92/2.10 dependent: set(auto1).
% 1.92/2.10 dependent: set(process_input).
% 1.92/2.10 dependent: clear(print_kept).
% 1.92/2.10 dependent: clear(print_new_demod).
% 1.92/2.10 dependent: clear(print_back_demod).
% 1.92/2.10 dependent: clear(print_back_sub).
% 1.92/2.10 dependent: set(control_memory).
% 1.92/2.10 dependent: assign(max_mem, 12000).
% 1.92/2.10 dependent: assign(pick_given_ratio, 4).
% 1.92/2.10 dependent: assign(stats_level, 1).
% 1.92/2.10 dependent: assign(max_seconds, 10800).
% 1.92/2.10 clear(print_given).
% 1.92/2.10
% 1.92/2.10 list(usable).
% 1.92/2.10 0 [] A=A.
% 1.92/2.10 0 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.92/2.10 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.92/2.10 0 [] inverse(A)=divide(divide(B,B),A).
% 1.92/2.10 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.92/2.10 end_of_list.
% 1.92/2.10
% 1.92/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.92/2.10
% 1.92/2.10 All clauses are units, and equality is present; the
% 1.92/2.10 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.92/2.10
% 1.92/2.10 dependent: set(knuth_bendix).
% 1.92/2.10 dependent: set(anl_eq).
% 1.92/2.10 dependent: set(para_from).
% 1.92/2.10 dependent: set(para_into).
% 1.92/2.10 dependent: clear(para_from_right).
% 1.92/2.10 dependent: clear(para_into_right).
% 1.92/2.10 dependent: set(para_from_vars).
% 1.92/2.10 dependent: set(eq_units_both_ways).
% 1.92/2.10 dependent: set(dynamic_demod_all).
% 1.92/2.10 dependent: set(dynamic_demod).
% 1.92/2.10 dependent: set(order_eq).
% 1.92/2.10 dependent: set(back_demod).
% 1.92/2.10 dependent: set(lrpo).
% 1.92/2.10
% 1.92/2.10 ------------> process usable:
% 1.92/2.10 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.92/2.10
% 1.92/2.10 ------------> process sos:
% 1.92/2.10 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.92/2.10 ** KEPT (pick-wt=11): 4 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.92/2.10 ---> New Demodulator: 5 [new_demod,4] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.92/2.10 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.92/2.10 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.92/2.10 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.92/2.10 >>>> Starting back demodulation with 5.
% 1.92/2.10 ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.92/2.10 ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.92/2.10 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.92/2.10 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.92/2.10
% 1.92/2.10 ======= end of input processing =======
% 1.92/2.10
% 1.92/2.10 =========== start of search ===========
% 1.92/2.10
% 1.92/2.10 -------- PROOF --------
% 1.92/2.10
% 1.92/2.10 ----> UNIT CONFLICT at 0.01 sec ----> 161 [binary,160.1,142.1] $F.
% 1.92/2.10
% 1.92/2.10 Length of proof is 23. Level of proof is 11.
% 1.92/2.10
% 1.92/2.10 ---------------- PROOF ----------------
% 1.92/2.10 % SZS status Unsatisfiable
% 1.92/2.10 % SZS output start Refutation
% See solution above
% 1.92/2.10 ------------ end of proof -------------
% 1.92/2.10
% 1.92/2.10
% 1.92/2.10 Search stopped by max_proofs option.
% 1.92/2.10
% 1.92/2.10
% 1.92/2.10 Search stopped by max_proofs option.
% 1.92/2.10
% 1.92/2.10 ============ end of search ============
% 1.92/2.10
% 1.92/2.10 -------------- statistics -------------
% 1.92/2.10 clauses given 19
% 1.92/2.10 clauses generated 187
% 1.92/2.10 clauses kept 107
% 1.92/2.10 clauses forward subsumed 194
% 1.92/2.10 clauses back subsumed 2
% 1.92/2.10 Kbytes malloced 1953
% 1.92/2.10
% 1.92/2.10 ----------- times (seconds) -----------
% 1.92/2.10 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.92/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.92/2.10
% 1.92/2.10 That finishes the proof of the theorem.
% 1.92/2.10
% 1.92/2.10 Process 6306 finished Wed Jul 27 05:22:35 2022
% 1.92/2.10 Otter interrupted
% 1.92/2.10 PROOF FOUND
%------------------------------------------------------------------------------