TSTP Solution File: GRP514-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 12:57:09 EDT 2022
% Result : Unsatisfiable 1.60s 1.79s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 3 RR)
% Number of literals : 15 ( 14 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP514-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP514-1.p',unknown),
[] ).
cnf(3,axiom,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B,
file('GRP514-1.p',unknown),
[] ).
cnf(5,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(multiply(D,C))))))) = D,
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.2.1,3.1.1')] ).
cnf(7,plain,
multiply(A,multiply(multiply(B,multiply(multiply(C,D),inverse(multiply(A,D)))),inverse(C))) = B,
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.2.2.1,3.1.1')] ).
cnf(17,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(para_into,[status(thm),theory(equality)],[5,3]),
[iquote('para_into,5.1.1.2.2.1,3.1.1')] ).
cnf(21,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(para_from,[status(thm),theory(equality)],[17,5]),
[iquote('para_from,17.1.1,5.1.1.2.2.1')] ).
cnf(25,plain,
multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) = A,
inference(para_from,[status(thm),theory(equality)],[21,5]),
[iquote('para_from,21.1.1,5.1.1.2.2.1')] ).
cnf(48,plain,
multiply(A,multiply(multiply(B,C),inverse(B))) = multiply(A,C),
inference(para_into,[status(thm),theory(equality)],[7,21]),
[iquote('para_into,7.1.1.2.1,21.1.1')] ).
cnf(63,plain,
multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),C) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,25]),48]),
[iquote('para_into,25.1.1.2.2.1,25.1.1,demod,48')] ).
cnf(123,plain,
multiply(A,multiply(B,inverse(multiply(B,inverse(C))))) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[63,48])]),
[iquote('para_from,63.1.1,47.1.1.2,flip.1')] ).
cnf(124,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[63,21]),123]),
[iquote('para_from,63.1.1,21.1.1.2,demod,123')] ).
cnf(150,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(para_from,[status(thm),theory(equality)],[124,17]),
[iquote('para_from,124.1.1,17.1.1.2')] ).
cnf(155,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[124,1]),150]),
[iquote('para_from,124.1.1,1.1.1,demod,150')] ).
cnf(156,plain,
$false,
inference(binary,[status(thm)],[155,2]),
[iquote('binary,155.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n016.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 05:29:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.60/1.79 ----- Otter 3.3f, August 2004 -----
% 1.60/1.79 The process was started by sandbox on n016.cluster.edu,
% 1.60/1.79 Wed Jul 27 05:29:07 2022
% 1.60/1.79 The command was "./otter". The process ID is 19040.
% 1.60/1.79
% 1.60/1.79 set(prolog_style_variables).
% 1.60/1.79 set(auto).
% 1.60/1.79 dependent: set(auto1).
% 1.60/1.79 dependent: set(process_input).
% 1.60/1.79 dependent: clear(print_kept).
% 1.60/1.79 dependent: clear(print_new_demod).
% 1.60/1.79 dependent: clear(print_back_demod).
% 1.60/1.79 dependent: clear(print_back_sub).
% 1.60/1.79 dependent: set(control_memory).
% 1.60/1.79 dependent: assign(max_mem, 12000).
% 1.60/1.79 dependent: assign(pick_given_ratio, 4).
% 1.60/1.79 dependent: assign(stats_level, 1).
% 1.60/1.79 dependent: assign(max_seconds, 10800).
% 1.60/1.79 clear(print_given).
% 1.60/1.79
% 1.60/1.79 list(usable).
% 1.60/1.79 0 [] A=A.
% 1.60/1.79 0 [] multiply(A,multiply(multiply(B,C),inverse(multiply(A,C))))=B.
% 1.60/1.79 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.60/1.79 end_of_list.
% 1.60/1.79
% 1.60/1.79 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.60/1.79
% 1.60/1.79 All clauses are units, and equality is present; the
% 1.60/1.79 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.60/1.79
% 1.60/1.79 dependent: set(knuth_bendix).
% 1.60/1.79 dependent: set(anl_eq).
% 1.60/1.79 dependent: set(para_from).
% 1.60/1.79 dependent: set(para_into).
% 1.60/1.79 dependent: clear(para_from_right).
% 1.60/1.79 dependent: clear(para_into_right).
% 1.60/1.79 dependent: set(para_from_vars).
% 1.60/1.79 dependent: set(eq_units_both_ways).
% 1.60/1.79 dependent: set(dynamic_demod_all).
% 1.60/1.79 dependent: set(dynamic_demod).
% 1.60/1.79 dependent: set(order_eq).
% 1.60/1.79 dependent: set(back_demod).
% 1.60/1.79 dependent: set(lrpo).
% 1.60/1.79
% 1.60/1.79 ------------> process usable:
% 1.60/1.79 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.60/1.79
% 1.60/1.79 ------------> process sos:
% 1.60/1.79 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.60/1.79 ** KEPT (pick-wt=12): 3 [] multiply(A,multiply(multiply(B,C),inverse(multiply(A,C))))=B.
% 1.60/1.79 ---> New Demodulator: 4 [new_demod,3] multiply(A,multiply(multiply(B,C),inverse(multiply(A,C))))=B.
% 1.60/1.79 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.60/1.79 >>>> Starting back demodulation with 4.
% 1.60/1.79
% 1.60/1.79 ======= end of input processing =======
% 1.60/1.79
% 1.60/1.79 =========== start of search ===========
% 1.60/1.79
% 1.60/1.79 -------- PROOF --------
% 1.60/1.79
% 1.60/1.79 ----> UNIT CONFLICT at 0.01 sec ----> 156 [binary,155.1,2.1] $F.
% 1.60/1.79
% 1.60/1.79 Length of proof is 11. Level of proof is 9.
% 1.60/1.79
% 1.60/1.79 ---------------- PROOF ----------------
% 1.60/1.79 % SZS status Unsatisfiable
% 1.60/1.79 % SZS output start Refutation
% See solution above
% 1.60/1.79 ------------ end of proof -------------
% 1.60/1.79
% 1.60/1.79
% 1.60/1.79 Search stopped by max_proofs option.
% 1.60/1.79
% 1.60/1.79
% 1.60/1.79 Search stopped by max_proofs option.
% 1.60/1.79
% 1.60/1.79 ============ end of search ============
% 1.60/1.79
% 1.60/1.79 -------------- statistics -------------
% 1.60/1.79 clauses given 10
% 1.60/1.79 clauses generated 146
% 1.60/1.79 clauses kept 82
% 1.60/1.79 clauses forward subsumed 115
% 1.60/1.79 clauses back subsumed 0
% 1.60/1.79 Kbytes malloced 1953
% 1.60/1.79
% 1.60/1.79 ----------- times (seconds) -----------
% 1.60/1.79 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.60/1.79 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.60/1.79 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.60/1.79
% 1.60/1.79 That finishes the proof of the theorem.
% 1.60/1.79
% 1.60/1.79 Process 19040 finished Wed Jul 27 05:29:08 2022
% 1.60/1.79 Otter interrupted
% 1.60/1.79 PROOF FOUND
%------------------------------------------------------------------------------