TSTP Solution File: RNG007-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0.
% 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 13:12:01 EDT 2022
% Result : Unsatisfiable 1.86s 2.06s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 2 RR)
% Number of literals : 14 ( 13 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 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 : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
add(a,a) != additive_identity,
file('RNG007-4.p',unknown),
[] ).
cnf(5,axiom,
add(additive_inverse(A),A) = additive_identity,
file('RNG007-4.p',unknown),
[] ).
cnf(14,axiom,
additive_inverse(additive_inverse(A)) = A,
file('RNG007-4.p',unknown),
[] ).
cnf(21,axiom,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
file('RNG007-4.p',unknown),
[] ).
cnf(23,plain,
additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(24,axiom,
multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)),
file('RNG007-4.p',unknown),
[] ).
cnf(25,plain,
multiply(additive_inverse(A),B) = multiply(A,additive_inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24]),23]),
[iquote('copy,24,demod,23')] ).
cnf(31,axiom,
multiply(A,A) = A,
file('RNG007-4.p',unknown),
[] ).
cnf(34,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(para_into,[status(thm),theory(equality)],[5,14]),
[iquote('para_into,5.1.1.1,13.1.1')] ).
cnf(45,plain,
multiply(A,additive_inverse(A)) = additive_inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,31])]),
[iquote('para_into,22.1.1.1,31.1.1,flip.1')] ).
cnf(48,plain,
multiply(additive_inverse(A),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[45,14]),14]),
[iquote('para_into,44.1.1.2,13.1.1,demod,14')] ).
cnf(68,plain,
additive_inverse(A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,48]),45])]),
[iquote('para_into,25.1.1,48.1.1,demod,45,flip.1')] ).
cnf(73,plain,
add(A,A) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[34]),68]),
[iquote('back_demod,34,demod,68')] ).
cnf(75,plain,
$false,
inference(binary,[status(thm)],[73,1]),
[iquote('binary,73.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 02:26:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.86/2.05 ----- Otter 3.3f, August 2004 -----
% 1.86/2.05 The process was started by sandbox on n023.cluster.edu,
% 1.86/2.05 Wed Jul 27 02:26:18 2022
% 1.86/2.05 The command was "./otter". The process ID is 9814.
% 1.86/2.05
% 1.86/2.05 set(prolog_style_variables).
% 1.86/2.05 set(auto).
% 1.86/2.05 dependent: set(auto1).
% 1.86/2.05 dependent: set(process_input).
% 1.86/2.05 dependent: clear(print_kept).
% 1.86/2.05 dependent: clear(print_new_demod).
% 1.86/2.05 dependent: clear(print_back_demod).
% 1.86/2.05 dependent: clear(print_back_sub).
% 1.86/2.05 dependent: set(control_memory).
% 1.86/2.05 dependent: assign(max_mem, 12000).
% 1.86/2.05 dependent: assign(pick_given_ratio, 4).
% 1.86/2.05 dependent: assign(stats_level, 1).
% 1.86/2.05 dependent: assign(max_seconds, 10800).
% 1.86/2.05 clear(print_given).
% 1.86/2.05
% 1.86/2.05 list(usable).
% 1.86/2.05 0 [] A=A.
% 1.86/2.05 0 [] add(additive_identity,X)=X.
% 1.86/2.05 0 [] add(additive_inverse(X),X)=additive_identity.
% 1.86/2.05 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.86/2.05 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.86/2.05 0 [] additive_inverse(additive_identity)=additive_identity.
% 1.86/2.05 0 [] additive_inverse(additive_inverse(X))=X.
% 1.86/2.05 0 [] multiply(X,additive_identity)=additive_identity.
% 1.86/2.05 0 [] multiply(additive_identity,X)=additive_identity.
% 1.86/2.05 0 [] additive_inverse(add(X,Y))=add(additive_inverse(X),additive_inverse(Y)).
% 1.86/2.05 0 [] multiply(X,additive_inverse(Y))=additive_inverse(multiply(X,Y)).
% 1.86/2.05 0 [] multiply(additive_inverse(X),Y)=additive_inverse(multiply(X,Y)).
% 1.86/2.05 0 [] add(add(X,Y),Z)=add(X,add(Y,Z)).
% 1.86/2.05 0 [] add(X,Y)=add(Y,X).
% 1.86/2.05 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.86/2.05 0 [] multiply(X,X)=X.
% 1.86/2.05 0 [] add(a,a)!=additive_identity.
% 1.86/2.05 end_of_list.
% 1.86/2.05
% 1.86/2.05 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.86/2.05
% 1.86/2.05 All clauses are units, and equality is present; the
% 1.86/2.05 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.86/2.05
% 1.86/2.05 dependent: set(knuth_bendix).
% 1.86/2.05 dependent: set(anl_eq).
% 1.86/2.05 dependent: set(para_from).
% 1.86/2.05 dependent: set(para_into).
% 1.86/2.05 dependent: clear(para_from_right).
% 1.86/2.05 dependent: clear(para_into_right).
% 1.86/2.05 dependent: set(para_from_vars).
% 1.86/2.05 dependent: set(eq_units_both_ways).
% 1.86/2.05 dependent: set(dynamic_demod_all).
% 1.86/2.05 dependent: set(dynamic_demod).
% 1.86/2.05 dependent: set(order_eq).
% 1.86/2.05 dependent: set(back_demod).
% 1.86/2.05 dependent: set(lrpo).
% 1.86/2.05
% 1.86/2.05 ------------> process usable:
% 1.86/2.05 ** KEPT (pick-wt=5): 1 [] add(a,a)!=additive_identity.
% 1.86/2.05
% 1.86/2.05 ------------> process sos:
% 1.86/2.05 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.86/2.05 ** KEPT (pick-wt=5): 3 [] add(additive_identity,A)=A.
% 1.86/2.05 ---> New Demodulator: 4 [new_demod,3] add(additive_identity,A)=A.
% 1.86/2.05 ** KEPT (pick-wt=6): 5 [] add(additive_inverse(A),A)=additive_identity.
% 1.86/2.05 ---> New Demodulator: 6 [new_demod,5] add(additive_inverse(A),A)=additive_identity.
% 1.86/2.05 ** KEPT (pick-wt=13): 7 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.86/2.05 ---> New Demodulator: 8 [new_demod,7] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.86/2.05 ** KEPT (pick-wt=13): 9 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.86/2.05 ---> New Demodulator: 10 [new_demod,9] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.86/2.05 ** KEPT (pick-wt=4): 11 [] additive_inverse(additive_identity)=additive_identity.
% 1.86/2.05 ---> New Demodulator: 12 [new_demod,11] additive_inverse(additive_identity)=additive_identity.
% 1.86/2.05 ** KEPT (pick-wt=5): 13 [] additive_inverse(additive_inverse(A))=A.
% 1.86/2.05 ---> New Demodulator: 14 [new_demod,13] additive_inverse(additive_inverse(A))=A.
% 1.86/2.05 ** KEPT (pick-wt=5): 15 [] multiply(A,additive_identity)=additive_identity.
% 1.86/2.05 ---> New Demodulator: 16 [new_demod,15] multiply(A,additive_identity)=additive_identity.
% 1.86/2.05 ** KEPT (pick-wt=5): 17 [] multiply(additive_identity,A)=additive_identity.
% 1.86/2.05 ---> New Demodulator: 18 [new_demod,17] multiply(additive_identity,A)=additive_identity.
% 1.86/2.05 ** KEPT (pick-wt=10): 19 [] additive_inverse(add(A,B))=add(additive_inverse(A),additive_inverse(B)).
% 1.86/2.05 ---> New Demodulator: 20 [new_demod,19] additive_inverse(add(A,B))=add(additive_inverse(A),additive_inverse(B)).
% 1.86/2.05 ** KEPT (pick-wt=9): 22 [copy,21,flip.1] additive_inverse(multiply(A,B))=multiply(A,additive_inverse(B)).
% 1.86/2.05 ---> New Demodulator: 23 [new_demod,22] additive_inverse(multiply(A,B))=multiply(A,additive_inverse(B)).
% 1.86/2.05 ** KEPT (pick-wt=9): 25 [copy,24,demod,23] multiply(additive_inverse(A),B)=multiply(A,additive_inverse(B)).
% 1.86/2.05 ** KEPT (pick-wt=11): 26 [] add(add(A,B),C)=add(A,add(B,C)).
% 1.86/2.06 ---> New Demodulator: 27 [new_demod,26] add(add(A,B),C)=add(A,add(B,C)).
% 1.86/2.06 ** KEPT (pick-wt=7): 28 [] add(A,B)=add(B,A).
% 1.86/2.06 ** KEPT (pick-wt=11): 29 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.86/2.06 ---> New Demodulator: 30 [new_demod,29] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.86/2.06 ** KEPT (pick-wt=5): 31 [] multiply(A,A)=A.
% 1.86/2.06 ---> New Demodulator: 32 [new_demod,31] multiply(A,A)=A.
% 1.86/2.06 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.86/2.06 >>>> Starting back demodulation with 4.
% 1.86/2.06 >>>> Starting back demodulation with 6.
% 1.86/2.06 >>>> Starting back demodulation with 8.
% 1.86/2.06 >>>> Starting back demodulation with 10.
% 1.86/2.06 >>>> Starting back demodulation with 12.
% 1.86/2.06 >>>> Starting back demodulation with 14.
% 1.86/2.06 >>>> Starting back demodulation with 16.
% 1.86/2.06 >>>> Starting back demodulation with 18.
% 1.86/2.06 >>>> Starting back demodulation with 20.
% 1.86/2.06 >>>> Starting back demodulation with 23.
% 1.86/2.06 ** KEPT (pick-wt=9): 33 [copy,25,flip.1] multiply(A,additive_inverse(B))=multiply(additive_inverse(A),B).
% 1.86/2.06 >>>> Starting back demodulation with 27.
% 1.86/2.06 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] add(A,B)=add(B,A).
% 1.86/2.06 >>>> Starting back demodulation with 30.
% 1.86/2.06 >>>> Starting back demodulation with 32.
% 1.86/2.06 Following clause subsumed by 25 during input processing: 0 [copy,33,flip.1] multiply(additive_inverse(A),B)=multiply(A,additive_inverse(B)).
% 1.86/2.06
% 1.86/2.06 ======= end of input processing =======
% 1.86/2.06
% 1.86/2.06 =========== start of search ===========
% 1.86/2.06
% 1.86/2.06 -------- PROOF --------
% 1.86/2.06
% 1.86/2.06 ----> UNIT CONFLICT at 0.00 sec ----> 75 [binary,73.1,1.1] $F.
% 1.86/2.06
% 1.86/2.06 Length of proof is 7. Level of proof is 5.
% 1.86/2.06
% 1.86/2.06 ---------------- PROOF ----------------
% 1.86/2.06 % SZS status Unsatisfiable
% 1.86/2.06 % SZS output start Refutation
% See solution above
% 1.86/2.06 ------------ end of proof -------------
% 1.86/2.06
% 1.86/2.06
% 1.86/2.06 Search stopped by max_proofs option.
% 1.86/2.06
% 1.86/2.06
% 1.86/2.06 Search stopped by max_proofs option.
% 1.86/2.06
% 1.86/2.06 ============ end of search ============
% 1.86/2.06
% 1.86/2.06 -------------- statistics -------------
% 1.86/2.06 clauses given 17
% 1.86/2.06 clauses generated 111
% 1.86/2.06 clauses kept 40
% 1.86/2.06 clauses forward subsumed 108
% 1.86/2.06 clauses back subsumed 0
% 1.86/2.06 Kbytes malloced 976
% 1.86/2.06
% 1.86/2.06 ----------- times (seconds) -----------
% 1.86/2.06 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.06 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.86/2.06
% 1.86/2.06 That finishes the proof of the theorem.
% 1.86/2.06
% 1.86/2.06 Process 9814 finished Wed Jul 27 02:26:20 2022
% 1.86/2.06 Otter interrupted
% 1.86/2.06 PROOF FOUND
%------------------------------------------------------------------------------