TSTP Solution File: RNG012-6 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG012-6 : TPTP v8.1.0. Released v1.0.0.
% 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 13:12:04 EDT 2022
% Result : Unsatisfiable 1.93s 2.11s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 2 RR)
% Number of literals : 20 ( 19 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 34 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(additive_inverse(a),additive_inverse(b)) != multiply(a,b),
file('RNG012-6.p',unknown),
[] ).
cnf(4,axiom,
add(additive_identity,A) = A,
file('RNG012-6.p',unknown),
[] ).
cnf(6,axiom,
add(A,additive_identity) = A,
file('RNG012-6.p',unknown),
[] ).
cnf(8,axiom,
multiply(additive_identity,A) = additive_identity,
file('RNG012-6.p',unknown),
[] ).
cnf(10,axiom,
multiply(A,additive_identity) = additive_identity,
file('RNG012-6.p',unknown),
[] ).
cnf(11,axiom,
add(additive_inverse(A),A) = additive_identity,
file('RNG012-6.p',unknown),
[] ).
cnf(13,axiom,
add(A,additive_inverse(A)) = additive_identity,
file('RNG012-6.p',unknown),
[] ).
cnf(17,axiom,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
file('RNG012-6.p',unknown),
[] ).
cnf(19,axiom,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
file('RNG012-6.p',unknown),
[] ).
cnf(21,axiom,
add(A,B) = add(B,A),
file('RNG012-6.p',unknown),
[] ).
cnf(22,axiom,
add(A,add(B,C)) = add(add(A,B),C),
file('RNG012-6.p',unknown),
[] ).
cnf(24,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
[iquote('copy,22,flip.1')] ).
cnf(37,plain,
add(multiply(A,B),multiply(A,additive_inverse(B))) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,13]),10])]),
[iquote('para_into,17.1.1.2,13.1.1,demod,10,flip.1')] ).
cnf(54,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,13]),4])]),
[iquote('para_into,23.1.1.1,13.1.1,demod,4,flip.1')] ).
cnf(56,plain,
add(additive_inverse(A),add(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,11]),4])]),
[iquote('para_into,23.1.1.1,11.1.1,demod,4,flip.1')] ).
cnf(66,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[54,21]),24]),
[iquote('para_into,54.1.1,21.1.1,demod,24')] ).
cnf(74,plain,
add(multiply(A,B),multiply(additive_inverse(A),B)) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,13]),8])]),
[iquote('para_into,19.1.1.1,13.1.1,demod,8,flip.1')] ).
cnf(87,plain,
additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[56,37]),6]),
[iquote('para_into,56.1.1.2,37.1.1,demod,6')] ).
cnf(162,plain,
multiply(additive_inverse(A),additive_inverse(B)) = multiply(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[74,66]),87,6]),
[iquote('para_from,74.1.1,66.1.1.2,demod,87,6')] ).
cnf(164,plain,
$false,
inference(binary,[status(thm)],[162,1]),
[iquote('binary,162.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG012-6 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 02:02:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.10 ----- Otter 3.3f, August 2004 -----
% 1.93/2.10 The process was started by sandbox on n011.cluster.edu,
% 1.93/2.10 Wed Jul 27 02:02:25 2022
% 1.93/2.10 The command was "./otter". The process ID is 25525.
% 1.93/2.10
% 1.93/2.10 set(prolog_style_variables).
% 1.93/2.10 set(auto).
% 1.93/2.10 dependent: set(auto1).
% 1.93/2.10 dependent: set(process_input).
% 1.93/2.10 dependent: clear(print_kept).
% 1.93/2.10 dependent: clear(print_new_demod).
% 1.93/2.10 dependent: clear(print_back_demod).
% 1.93/2.10 dependent: clear(print_back_sub).
% 1.93/2.10 dependent: set(control_memory).
% 1.93/2.10 dependent: assign(max_mem, 12000).
% 1.93/2.10 dependent: assign(pick_given_ratio, 4).
% 1.93/2.10 dependent: assign(stats_level, 1).
% 1.93/2.10 dependent: assign(max_seconds, 10800).
% 1.93/2.10 clear(print_given).
% 1.93/2.10
% 1.93/2.10 list(usable).
% 1.93/2.10 0 [] A=A.
% 1.93/2.10 0 [] add(additive_identity,X)=X.
% 1.93/2.10 0 [] add(X,additive_identity)=X.
% 1.93/2.10 0 [] multiply(additive_identity,X)=additive_identity.
% 1.93/2.10 0 [] multiply(X,additive_identity)=additive_identity.
% 1.93/2.10 0 [] add(additive_inverse(X),X)=additive_identity.
% 1.93/2.10 0 [] add(X,additive_inverse(X))=additive_identity.
% 1.93/2.10 0 [] additive_inverse(additive_inverse(X))=X.
% 1.93/2.10 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.93/2.10 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.93/2.10 0 [] add(X,Y)=add(Y,X).
% 1.93/2.10 0 [] add(X,add(Y,Z))=add(add(X,Y),Z).
% 1.93/2.10 0 [] multiply(multiply(X,Y),Y)=multiply(X,multiply(Y,Y)).
% 1.93/2.10 0 [] multiply(multiply(X,X),Y)=multiply(X,multiply(X,Y)).
% 1.93/2.10 0 [] associator(X,Y,Z)=add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))).
% 1.93/2.10 0 [] commutator(X,Y)=add(multiply(Y,X),additive_inverse(multiply(X,Y))).
% 1.93/2.10 0 [] multiply(additive_inverse(a),additive_inverse(b))!=multiply(a,b).
% 1.93/2.10 end_of_list.
% 1.93/2.10
% 1.93/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.93/2.10
% 1.93/2.10 All clauses are units, and equality is present; the
% 1.93/2.10 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.93/2.10
% 1.93/2.10 dependent: set(knuth_bendix).
% 1.93/2.10 dependent: set(anl_eq).
% 1.93/2.10 dependent: set(para_from).
% 1.93/2.10 dependent: set(para_into).
% 1.93/2.10 dependent: clear(para_from_right).
% 1.93/2.10 dependent: clear(para_into_right).
% 1.93/2.10 dependent: set(para_from_vars).
% 1.93/2.10 dependent: set(eq_units_both_ways).
% 1.93/2.10 dependent: set(dynamic_demod_all).
% 1.93/2.10 dependent: set(dynamic_demod).
% 1.93/2.10 dependent: set(order_eq).
% 1.93/2.10 dependent: set(back_demod).
% 1.93/2.10 dependent: set(lrpo).
% 1.93/2.10
% 1.93/2.10 ------------> process usable:
% 1.93/2.10 ** KEPT (pick-wt=9): 1 [] multiply(additive_inverse(a),additive_inverse(b))!=multiply(a,b).
% 1.93/2.10
% 1.93/2.10 ------------> process sos:
% 1.93/2.10 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.93/2.10 ** KEPT (pick-wt=5): 3 [] add(additive_identity,A)=A.
% 1.93/2.10 ---> New Demodulator: 4 [new_demod,3] add(additive_identity,A)=A.
% 1.93/2.10 ** KEPT (pick-wt=5): 5 [] add(A,additive_identity)=A.
% 1.93/2.10 ---> New Demodulator: 6 [new_demod,5] add(A,additive_identity)=A.
% 1.93/2.10 ** KEPT (pick-wt=5): 7 [] multiply(additive_identity,A)=additive_identity.
% 1.93/2.10 ---> New Demodulator: 8 [new_demod,7] multiply(additive_identity,A)=additive_identity.
% 1.93/2.10 ** KEPT (pick-wt=5): 9 [] multiply(A,additive_identity)=additive_identity.
% 1.93/2.10 ---> New Demodulator: 10 [new_demod,9] multiply(A,additive_identity)=additive_identity.
% 1.93/2.10 ** KEPT (pick-wt=6): 11 [] add(additive_inverse(A),A)=additive_identity.
% 1.93/2.10 ---> New Demodulator: 12 [new_demod,11] add(additive_inverse(A),A)=additive_identity.
% 1.93/2.10 ** KEPT (pick-wt=6): 13 [] add(A,additive_inverse(A))=additive_identity.
% 1.93/2.10 ---> New Demodulator: 14 [new_demod,13] add(A,additive_inverse(A))=additive_identity.
% 1.93/2.10 ** KEPT (pick-wt=5): 15 [] additive_inverse(additive_inverse(A))=A.
% 1.93/2.10 ---> New Demodulator: 16 [new_demod,15] additive_inverse(additive_inverse(A))=A.
% 1.93/2.10 ** KEPT (pick-wt=13): 17 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.93/2.10 ---> New Demodulator: 18 [new_demod,17] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.93/2.10 ** KEPT (pick-wt=13): 19 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.93/2.10 ---> New Demodulator: 20 [new_demod,19] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.93/2.10 ** KEPT (pick-wt=7): 21 [] add(A,B)=add(B,A).
% 1.93/2.10 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] add(add(A,B),C)=add(A,add(B,C)).
% 1.93/2.10 ---> New Demodulator: 24 [new_demod,23] add(add(A,B),C)=add(A,add(B,C)).
% 1.93/2.10 ** KEPT (pick-wt=11): 25 [] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.93/2.10 ---> New Demodulator: 26 [new_demod,25] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.93/2.10 ** KEPT (pick-wt=11): 27 [] multiply(multiply(A,A),B)=multiply(A,multiply(A,B)).
% 1.93/2.11 ---> New Demodulator: 28 [new_demod,27] multiply(multiply(A,A),B)=multiply(A,multiply(A,B)).
% 1.93/2.11 ** KEPT (pick-wt=17): 30 [copy,29,flip.1] add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C))))=associator(A,B,C).
% 1.93/2.11 ---> New Demodulator: 31 [new_demod,30] add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C))))=associator(A,B,C).
% 1.93/2.11 ** KEPT (pick-wt=12): 33 [copy,32,flip.1] add(multiply(A,B),additive_inverse(multiply(B,A)))=commutator(B,A).
% 1.93/2.11 ---> New Demodulator: 34 [new_demod,33] add(multiply(A,B),additive_inverse(multiply(B,A)))=commutator(B,A).
% 1.93/2.11 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.93/2.11 >>>> Starting back demodulation with 4.
% 1.93/2.11 >>>> Starting back demodulation with 6.
% 1.93/2.11 >>>> Starting back demodulation with 8.
% 1.93/2.11 >>>> Starting back demodulation with 10.
% 1.93/2.11 >>>> Starting back demodulation with 12.
% 1.93/2.11 >>>> Starting back demodulation with 14.
% 1.93/2.11 >>>> Starting back demodulation with 16.
% 1.93/2.11 >>>> Starting back demodulation with 18.
% 1.93/2.11 >>>> Starting back demodulation with 20.
% 1.93/2.11 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] add(A,B)=add(B,A).
% 1.93/2.11 >>>> Starting back demodulation with 24.
% 1.93/2.11 >>>> Starting back demodulation with 26.
% 1.93/2.11 >>>> Starting back demodulation with 28.
% 1.93/2.11 >>>> Starting back demodulation with 31.
% 1.93/2.11 >>>> Starting back demodulation with 34.
% 1.93/2.11
% 1.93/2.11 ======= end of input processing =======
% 1.93/2.11
% 1.93/2.11 =========== start of search ===========
% 1.93/2.11
% 1.93/2.11 -------- PROOF --------
% 1.93/2.11
% 1.93/2.11 ----> UNIT CONFLICT at 0.00 sec ----> 164 [binary,162.1,1.1] $F.
% 1.93/2.11
% 1.93/2.11 Length of proof is 8. Level of proof is 4.
% 1.93/2.11
% 1.93/2.11 ---------------- PROOF ----------------
% 1.93/2.11 % SZS status Unsatisfiable
% 1.93/2.11 % SZS output start Refutation
% See solution above
% 1.93/2.11 ------------ end of proof -------------
% 1.93/2.11
% 1.93/2.11
% 1.93/2.11 Search stopped by max_proofs option.
% 1.93/2.11
% 1.93/2.11
% 1.93/2.11 Search stopped by max_proofs option.
% 1.93/2.11
% 1.93/2.11 ============ end of search ============
% 1.93/2.11
% 1.93/2.11 -------------- statistics -------------
% 1.93/2.11 clauses given 27
% 1.93/2.11 clauses generated 295
% 1.93/2.11 clauses kept 84
% 1.93/2.11 clauses forward subsumed 253
% 1.93/2.11 clauses back subsumed 0
% 1.93/2.11 Kbytes malloced 1953
% 1.93/2.11
% 1.93/2.11 ----------- times (seconds) -----------
% 1.93/2.11 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.11 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.93/2.11
% 1.93/2.11 That finishes the proof of the theorem.
% 1.93/2.11
% 1.93/2.11 Process 25525 finished Wed Jul 27 02:02:27 2022
% 1.93/2.11 Otter interrupted
% 1.93/2.11 PROOF FOUND
%------------------------------------------------------------------------------