%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG016-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 1.67s 1.83s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 6 RR)
% Number of literals : 22 ( 21 equ; 5 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))),
file('RNG016-6.p',unknown),
[] ).
cnf(2,plain,
add(multiply(x,z),additive_inverse(multiply(y,z))) != multiply(add(x,additive_inverse(y)),z),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
A = A,
file('RNG016-6.p',unknown),
[] ).
cnf(5,axiom,
add(additive_identity,A) = A,
file('RNG016-6.p',unknown),
[] ).
cnf(7,axiom,
add(A,additive_identity) = A,
file('RNG016-6.p',unknown),
[] ).
cnf(9,axiom,
multiply(additive_identity,A) = additive_identity,
file('RNG016-6.p',unknown),
[] ).
cnf(11,axiom,
multiply(A,additive_identity) = additive_identity,
file('RNG016-6.p',unknown),
[] ).
cnf(12,axiom,
add(additive_inverse(A),A) = additive_identity,
file('RNG016-6.p',unknown),
[] ).
cnf(14,axiom,
add(A,additive_inverse(A)) = additive_identity,
file('RNG016-6.p',unknown),
[] ).
cnf(18,axiom,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
file('RNG016-6.p',unknown),
[] ).
cnf(21,axiom,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
file('RNG016-6.p',unknown),
[] ).
cnf(23,axiom,
add(A,add(B,C)) = add(add(A,B),C),
file('RNG016-6.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)],[23])]),
[iquote('copy,23,flip.1')] ).
cnf(36,plain,
add(multiply(x,z),additive_inverse(multiply(y,z))) != add(multiply(x,z),multiply(additive_inverse(y),z)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),21]),
[iquote('back_demod,2,demod,21')] ).
cnf(39,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)],[18,14]),11])]),
[iquote('para_into,18.1.1.2,14.1.1,demod,11,flip.1')] ).
cnf(58,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)],[24,12]),5])]),
[iquote('para_into,24.1.1.1,12.1.1,demod,5,flip.1')] ).
cnf(76,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)],[21,14]),9])]),
[iquote('para_into,20.1.1.1,14.1.1,demod,9,flip.1')] ).
cnf(89,plain,
additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[58,39]),7]),
[iquote('para_into,58.1.1.2,39.1.1,demod,7')] ).
cnf(92,plain,
add(multiply(x,z),multiply(y,additive_inverse(z))) != add(multiply(x,z),multiply(additive_inverse(y),z)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[36]),89]),
[iquote('back_demod,36,demod,89')] ).
cnf(167,plain,
multiply(A,additive_inverse(B)) = multiply(additive_inverse(A),B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[76,58]),89,7]),
[iquote('para_from,76.1.1,58.1.1.2,demod,89,7')] ).
cnf(463,plain,
add(multiply(x,z),multiply(additive_inverse(y),z)) != add(multiply(x,z),multiply(additive_inverse(y),z)),
inference(para_into,[status(thm),theory(equality)],[92,167]),
[iquote('para_into,92.1.1.2,167.1.1')] ).
cnf(464,plain,
$false,
inference(binary,[status(thm)],[463,3]),
[iquote('binary,463.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG016-6 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 02:22:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.61/1.81 ----- Otter 3.3f, August 2004 -----
% 1.61/1.81 The process was started by sandbox2 on n028.cluster.edu,
% 1.61/1.81 Wed Jul 27 02:22:48 2022
% 1.61/1.81 The command was "./otter". The process ID is 1392.
% 1.61/1.81
% 1.61/1.81 set(prolog_style_variables).
% 1.61/1.81 set(auto).
% 1.61/1.81 dependent: set(auto1).
% 1.61/1.81 dependent: set(process_input).
% 1.61/1.81 dependent: clear(print_kept).
% 1.61/1.81 dependent: clear(print_new_demod).
% 1.61/1.81 dependent: clear(print_back_demod).
% 1.61/1.81 dependent: clear(print_back_sub).
% 1.61/1.81 dependent: set(control_memory).
% 1.61/1.81 dependent: assign(max_mem, 12000).
% 1.61/1.81 dependent: assign(pick_given_ratio, 4).
% 1.61/1.81 dependent: assign(stats_level, 1).
% 1.61/1.81 dependent: assign(max_seconds, 10800).
% 1.61/1.81 clear(print_given).
% 1.61/1.81
% 1.61/1.81 list(usable).
% 1.61/1.81 0 [] A=A.
% 1.61/1.81 0 [] add(additive_identity,X)=X.
% 1.61/1.81 0 [] add(X,additive_identity)=X.
% 1.61/1.81 0 [] multiply(additive_identity,X)=additive_identity.
% 1.61/1.81 0 [] multiply(X,additive_identity)=additive_identity.
% 1.61/1.81 0 [] add(additive_inverse(X),X)=additive_identity.
% 1.61/1.81 0 [] add(X,additive_inverse(X))=additive_identity.
% 1.61/1.81 0 [] additive_inverse(additive_inverse(X))=X.
% 1.61/1.81 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.61/1.81 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.61/1.81 0 [] add(X,Y)=add(Y,X).
% 1.61/1.81 0 [] add(X,add(Y,Z))=add(add(X,Y),Z).
% 1.61/1.81 0 [] multiply(multiply(X,Y),Y)=multiply(X,multiply(Y,Y)).
% 1.61/1.81 0 [] multiply(multiply(X,X),Y)=multiply(X,multiply(X,Y)).
% 1.61/1.81 0 [] associator(X,Y,Z)=add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))).
% 1.61/1.81 0 [] commutator(X,Y)=add(multiply(Y,X),additive_inverse(multiply(X,Y))).
% 1.61/1.81 0 [] multiply(add(x,additive_inverse(y)),z)!=add(multiply(x,z),additive_inverse(multiply(y,z))).
% 1.61/1.81 end_of_list.
% 1.61/1.81
% 1.61/1.81 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.61/1.81
% 1.61/1.81 All clauses are units, and equality is present; the
% 1.61/1.81 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.61/1.81
% 1.61/1.81 dependent: set(knuth_bendix).
% 1.61/1.81 dependent: set(anl_eq).
% 1.61/1.81 dependent: set(para_from).
% 1.61/1.81 dependent: set(para_into).
% 1.61/1.81 dependent: clear(para_from_right).
% 1.61/1.81 dependent: clear(para_into_right).
% 1.61/1.81 dependent: set(para_from_vars).
% 1.61/1.81 dependent: set(eq_units_both_ways).
% 1.61/1.81 dependent: set(dynamic_demod_all).
% 1.61/1.81 dependent: set(dynamic_demod).
% 1.61/1.81 dependent: set(order_eq).
% 1.61/1.81 dependent: set(back_demod).
% 1.61/1.81 dependent: set(lrpo).
% 1.61/1.81
% 1.61/1.81 ------------> process usable:
% 1.61/1.81 ** KEPT (pick-wt=15): 2 [copy,1,flip.1] add(multiply(x,z),additive_inverse(multiply(y,z)))!=multiply(add(x,additive_inverse(y)),z).
% 1.61/1.81
% 1.61/1.81 ------------> process sos:
% 1.61/1.81 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.61/1.81 ** KEPT (pick-wt=5): 4 [] add(additive_identity,A)=A.
% 1.61/1.81 ---> New Demodulator: 5 [new_demod,4] add(additive_identity,A)=A.
% 1.61/1.81 ** KEPT (pick-wt=5): 6 [] add(A,additive_identity)=A.
% 1.61/1.81 ---> New Demodulator: 7 [new_demod,6] add(A,additive_identity)=A.
% 1.61/1.81 ** KEPT (pick-wt=5): 8 [] multiply(additive_identity,A)=additive_identity.
% 1.61/1.81 ---> New Demodulator: 9 [new_demod,8] multiply(additive_identity,A)=additive_identity.
% 1.61/1.81 ** KEPT (pick-wt=5): 10 [] multiply(A,additive_identity)=additive_identity.
% 1.61/1.81 ---> New Demodulator: 11 [new_demod,10] multiply(A,additive_identity)=additive_identity.
% 1.61/1.81 ** KEPT (pick-wt=6): 12 [] add(additive_inverse(A),A)=additive_identity.
% 1.61/1.81 ---> New Demodulator: 13 [new_demod,12] add(additive_inverse(A),A)=additive_identity.
% 1.61/1.81 ** KEPT (pick-wt=6): 14 [] add(A,additive_inverse(A))=additive_identity.
% 1.61/1.81 ---> New Demodulator: 15 [new_demod,14] add(A,additive_inverse(A))=additive_identity.
% 1.61/1.81 ** KEPT (pick-wt=5): 16 [] additive_inverse(additive_inverse(A))=A.
% 1.61/1.81 ---> New Demodulator: 17 [new_demod,16] additive_inverse(additive_inverse(A))=A.
% 1.61/1.81 ** KEPT (pick-wt=13): 18 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.61/1.81 ---> New Demodulator: 19 [new_demod,18] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.61/1.81 ** KEPT (pick-wt=13): 20 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.61/1.81 ---> New Demodulator: 21 [new_demod,20] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.61/1.81 ** KEPT (pick-wt=7): 22 [] add(A,B)=add(B,A).
% 1.61/1.81 ** KEPT (pick-wt=11): 24 [copy,23,flip.1] add(add(A,B),C)=add(A,add(B,C)).
% 1.61/1.81 ---> New Demodulator: 25 [new_demod,24] add(add(A,B),C)=add(A,add(B,C)).
% 1.61/1.81 ** KEPT (pick-wt=11): 26 [] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.61/1.81 ---> New Demodulator: 27 [new_demod,26] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.67/1.83 ** KEPT (pick-wt=11): 28 [] multiply(multiply(A,A),B)=multiply(A,multiply(A,B)).
% 1.67/1.83 ---> New Demodulator: 29 [new_demod,28] multiply(multiply(A,A),B)=multiply(A,multiply(A,B)).
% 1.67/1.83 ** KEPT (pick-wt=17): 31 [copy,30,flip.1] add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C))))=associator(A,B,C).
% 1.67/1.83 ---> New Demodulator: 32 [new_demod,31] add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C))))=associator(A,B,C).
% 1.67/1.83 ** KEPT (pick-wt=12): 34 [copy,33,flip.1] add(multiply(A,B),additive_inverse(multiply(B,A)))=commutator(B,A).
% 1.67/1.83 ---> New Demodulator: 35 [new_demod,34] add(multiply(A,B),additive_inverse(multiply(B,A)))=commutator(B,A).
% 1.67/1.83 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.67/1.83 >>>> Starting back demodulation with 5.
% 1.67/1.83 >>>> Starting back demodulation with 7.
% 1.67/1.83 >>>> Starting back demodulation with 9.
% 1.67/1.83 >>>> Starting back demodulation with 11.
% 1.67/1.83 >>>> Starting back demodulation with 13.
% 1.67/1.83 >>>> Starting back demodulation with 15.
% 1.67/1.83 >>>> Starting back demodulation with 17.
% 1.67/1.83 >>>> Starting back demodulation with 19.
% 1.67/1.83 >>>> Starting back demodulation with 21.
% 1.67/1.83 >> back demodulating 2 with 21.
% 1.67/1.83 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] add(A,B)=add(B,A).
% 1.67/1.83 >>>> Starting back demodulation with 25.
% 1.67/1.83 >>>> Starting back demodulation with 27.
% 1.67/1.83 >>>> Starting back demodulation with 29.
% 1.67/1.83 >>>> Starting back demodulation with 32.
% 1.67/1.83 >>>> Starting back demodulation with 35.
% 1.67/1.83
% 1.67/1.83 ======= end of input processing =======
% 1.67/1.83
% 1.67/1.83 =========== start of search ===========
% 1.67/1.83
% 1.67/1.83 -------- PROOF --------
% 1.67/1.83
% 1.67/1.83 ----> UNIT CONFLICT at 0.02 sec ----> 464 [binary,463.1,3.1] $F.
% 1.67/1.83
% 1.67/1.83 Length of proof is 10. Level of proof is 5.
% 1.67/1.83
% 1.67/1.83 ---------------- PROOF ----------------
% 1.67/1.83 % SZS status Unsatisfiable
% 1.67/1.83 % SZS output start Refutation
% See solution above
% 1.67/1.83 ------------ end of proof -------------
% 1.67/1.83
% 1.67/1.83
% 1.67/1.83 Search stopped by max_proofs option.
% 1.67/1.83
% 1.67/1.83
% 1.67/1.83 Search stopped by max_proofs option.
% 1.67/1.83
% 1.67/1.83 ============ end of search ============
% 1.67/1.83
% 1.67/1.83 -------------- statistics -------------
% 1.67/1.83 clauses given 56
% 1.67/1.83 clauses generated 1163
% 1.67/1.83 clauses kept 271
% 1.67/1.83 clauses forward subsumed 1047
% 1.67/1.83 clauses back subsumed 4
% 1.67/1.83 Kbytes malloced 2929
% 1.67/1.83
% 1.67/1.83 ----------- times (seconds) -----------
% 1.67/1.83 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.67/1.83 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.83 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.67/1.83
% 1.67/1.83 That finishes the proof of the theorem.
% 1.67/1.83
% 1.67/1.83 Process 1392 finished Wed Jul 27 02:22:50 2022
% 1.67/1.83 Otter interrupted
% 1.67/1.83 PROOF FOUND
%------------------------------------------------------------------------------