TSTP Solution File: BOO034-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO034-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:47:38 EDT 2022
% Result : Unsatisfiable 4.48s 4.66s
% Output : Refutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 7 RR)
% Number of literals : 37 ( 36 equ; 6 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 : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 81 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b,
file('BOO034-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('BOO034-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(multiply(A,B,C),D,multiply(A,B,E)) = multiply(A,B,multiply(C,D,E)),
file('BOO034-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B,B) = B,
file('BOO034-1.p',unknown),
[] ).
cnf(8,axiom,
multiply(A,A,B) = A,
file('BOO034-1.p',unknown),
[] ).
cnf(9,axiom,
multiply(inverse(A),A,B) = B,
file('BOO034-1.p',unknown),
[] ).
cnf(12,axiom,
multiply(A,B,inverse(B)) = A,
file('BOO034-1.p',unknown),
[] ).
cnf(13,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),4]),
[iquote('back_demod,1,demod,4')] ).
cnf(14,plain,
multiply(A,B,multiply(A,C,D)) = multiply(A,C,multiply(inverse(C),B,D)),
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,3.1.1.1,11.1.1')] ).
cnf(16,plain,
multiply(A,B,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,8]),8,8]),
[iquote('para_into,3.1.1.1,7.1.1,demod,8,8')] ).
cnf(17,plain,
multiply(A,B,multiply(C,A,D)) = multiply(C,A,multiply(A,B,D)),
inference(para_into,[status(thm),theory(equality)],[4,6]),
[iquote('para_into,3.1.1.1,5.1.1')] ).
cnf(33,plain,
multiply(multiply(A,B,C),D,A) = multiply(A,B,multiply(C,D,A)),
inference(para_from,[status(thm),theory(equality)],[16,4]),
[iquote('para_from,15.1.1,3.1.1.3')] ).
cnf(40,plain,
multiply(A,B,C) = multiply(C,A,multiply(A,B,inverse(A))),
inference(para_into,[status(thm),theory(equality)],[17,12]),
[iquote('para_into,17.1.1.3,11.1.1')] ).
cnf(43,plain,
multiply(A,B,multiply(B,C,inverse(B))) = multiply(B,C,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[40])]),
[iquote('copy,40,flip.1')] ).
cnf(58,plain,
multiply(multiply(A,B,C),B,multiply(B,D,inverse(B))) = multiply(A,B,multiply(B,D,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[40,17])]),
[iquote('para_into,40.1.1,17.1.1,flip.1')] ).
cnf(59,plain,
multiply(inverse(A),B,multiply(B,A,inverse(B))) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[40,12])]),
[iquote('para_into,40.1.1,11.1.1,flip.1')] ).
cnf(61,plain,
multiply(A,B,multiply(B,A,inverse(B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[40,6])]),
[iquote('para_into,40.1.1,5.1.1,flip.1')] ).
cnf(73,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(c,d,multiply(d,multiply(g,f,e),inverse(d)))) != b,
inference(para_into,[status(thm),theory(equality)],[13,40]),
[iquote('para_into,13.1.1.3,40.1.1')] ).
cnf(78,plain,
multiply(A,B,multiply(C,D,multiply(B,A,inverse(B)))) = multiply(A,B,multiply(C,D,A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[61,4]),33])]),
[iquote('para_from,61.1.1,3.1.1.3,demod,33,flip.1')] ).
cnf(81,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[59,6]),12]),
[iquote('para_into,59.1.1.3,5.1.1,demod,12')] ).
cnf(98,plain,
multiply(A,inverse(B),B) = A,
inference(para_from,[status(thm),theory(equality)],[81,12]),
[iquote('para_from,81.1.1,11.1.1.3')] ).
cnf(102,plain,
multiply(A,inverse(A),B) = B,
inference(para_from,[status(thm),theory(equality)],[81,9]),
[iquote('para_from,81.1.1,9.1.1.1')] ).
cnf(104,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(c,d,multiply(d,multiply(g,f,e),inverse(d)))) != b,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[73]),102]),
[iquote('back_demod,73,demod,102')] ).
cnf(118,plain,
multiply(A,B,multiply(inverse(B),C,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,61]),16,78])]),
[iquote('para_into,14.1.1.3,61.1.1,demod,16,78,flip.1')] ).
cnf(125,plain,
multiply(A,B,C) = multiply(A,C,multiply(inverse(C),B,C)),
inference(para_into,[status(thm),theory(equality)],[14,6]),
[iquote('para_into,14.1.1.3,5.1.1')] ).
cnf(131,plain,
multiply(A,B,multiply(inverse(B),A,C)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,8])]),
[iquote('para_into,14.1.1,7.1.1,flip.1')] ).
cnf(138,plain,
multiply(A,B,multiply(inverse(B),C,B)) = multiply(A,C,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[125])]),
[iquote('copy,125,flip.1')] ).
cnf(154,plain,
multiply(A,B,multiply(inverse(A),B,A)) = multiply(A,B,inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[118,59]),33]),
[iquote('para_into,118.1.1.3,59.1.1,demod,33')] ).
cnf(180,plain,
multiply(inverse(A),B,multiply(B,A,C)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[131,40]),58]),
[iquote('para_into,131.1.1,40.1.1,demod,58')] ).
cnf(363,plain,
multiply(inverse(A),B,A) = B,
inference(para_into,[status(thm),theory(equality)],[180,6]),
[iquote('para_into,180.1.1.3,5.1.1')] ).
cnf(369,plain,
multiply(A,B,inverse(A)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[154]),363,6])]),
[iquote('back_demod,154,demod,363,6,flip.1')] ).
cnf(370,plain,
multiply(A,B,C) = multiply(A,C,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[138]),363]),
[iquote('back_demod,138,demod,363')] ).
cnf(394,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(c,d,multiply(g,f,e))) != b,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[104]),369]),
[iquote('back_demod,104,demod,369')] ).
cnf(407,plain,
multiply(A,B,C) = multiply(B,C,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[43]),369]),
[iquote('back_demod,43,demod,369')] ).
cnf(516,plain,
multiply(A,B,C) = multiply(C,B,A),
inference(para_into,[status(thm),theory(equality)],[407,370]),
[iquote('para_into,407.1.1,370.1.1')] ).
cnf(1849,plain,
b != b,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[394,516]),98]),
[iquote('para_into,394.1.1.2.1.3,516.1.1,demod,98')] ).
cnf(1850,plain,
$false,
inference(binary,[status(thm)],[1849,2]),
[iquote('binary,1849.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : BOO034-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 02:33:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 4.48/4.66 ----- Otter 3.3f, August 2004 -----
% 4.48/4.66 The process was started by sandbox on n022.cluster.edu,
% 4.48/4.66 Wed Jul 27 02:33:35 2022
% 4.48/4.66 The command was "./otter". The process ID is 30324.
% 4.48/4.66
% 4.48/4.66 set(prolog_style_variables).
% 4.48/4.66 set(auto).
% 4.48/4.66 dependent: set(auto1).
% 4.48/4.66 dependent: set(process_input).
% 4.48/4.66 dependent: clear(print_kept).
% 4.48/4.66 dependent: clear(print_new_demod).
% 4.48/4.66 dependent: clear(print_back_demod).
% 4.48/4.66 dependent: clear(print_back_sub).
% 4.48/4.66 dependent: set(control_memory).
% 4.48/4.66 dependent: assign(max_mem, 12000).
% 4.48/4.66 dependent: assign(pick_given_ratio, 4).
% 4.48/4.66 dependent: assign(stats_level, 1).
% 4.48/4.66 dependent: assign(max_seconds, 10800).
% 4.48/4.66 clear(print_given).
% 4.48/4.66
% 4.48/4.66 list(usable).
% 4.48/4.66 0 [] A=A.
% 4.48/4.66 0 [] multiply(multiply(V,W,X),Y,multiply(V,W,Z))=multiply(V,W,multiply(X,Y,Z)).
% 4.48/4.66 0 [] multiply(Y,X,X)=X.
% 4.48/4.66 0 [] multiply(X,X,Y)=X.
% 4.48/4.66 0 [] multiply(inverse(Y),Y,X)=X.
% 4.48/4.66 0 [] multiply(X,Y,inverse(Y))=X.
% 4.48/4.66 0 [] multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c))!=b.
% 4.48/4.66 end_of_list.
% 4.48/4.66
% 4.48/4.66 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 4.48/4.66
% 4.48/4.66 All clauses are units, and equality is present; the
% 4.48/4.66 strategy will be Knuth-Bendix with positive clauses in sos.
% 4.48/4.66
% 4.48/4.66 dependent: set(knuth_bendix).
% 4.48/4.66 dependent: set(anl_eq).
% 4.48/4.66 dependent: set(para_from).
% 4.48/4.66 dependent: set(para_into).
% 4.48/4.66 dependent: clear(para_from_right).
% 4.48/4.66 dependent: clear(para_into_right).
% 4.48/4.66 dependent: set(para_from_vars).
% 4.48/4.66 dependent: set(eq_units_both_ways).
% 4.48/4.66 dependent: set(dynamic_demod_all).
% 4.48/4.66 dependent: set(dynamic_demod).
% 4.48/4.66 dependent: set(order_eq).
% 4.48/4.66 dependent: set(back_demod).
% 4.48/4.66 dependent: set(lrpo).
% 4.48/4.66
% 4.48/4.66 ------------> process usable:
% 4.48/4.66 ** KEPT (pick-wt=26): 1 [] multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c))!=b.
% 4.48/4.66
% 4.48/4.66 ------------> process sos:
% 4.48/4.66 ** KEPT (pick-wt=3): 2 [] A=A.
% 4.48/4.66 ** KEPT (pick-wt=18): 3 [] multiply(multiply(A,B,C),D,multiply(A,B,E))=multiply(A,B,multiply(C,D,E)).
% 4.48/4.66 ---> New Demodulator: 4 [new_demod,3] multiply(multiply(A,B,C),D,multiply(A,B,E))=multiply(A,B,multiply(C,D,E)).
% 4.48/4.66 ** KEPT (pick-wt=6): 5 [] multiply(A,B,B)=B.
% 4.48/4.66 ---> New Demodulator: 6 [new_demod,5] multiply(A,B,B)=B.
% 4.48/4.66 ** KEPT (pick-wt=6): 7 [] multiply(A,A,B)=A.
% 4.48/4.66 ---> New Demodulator: 8 [new_demod,7] multiply(A,A,B)=A.
% 4.48/4.66 ** KEPT (pick-wt=7): 9 [] multiply(inverse(A),A,B)=B.
% 4.48/4.66 ---> New Demodulator: 10 [new_demod,9] multiply(inverse(A),A,B)=B.
% 4.48/4.66 ** KEPT (pick-wt=7): 11 [] multiply(A,B,inverse(B))=A.
% 4.48/4.66 ---> New Demodulator: 12 [new_demod,11] multiply(A,B,inverse(B))=A.
% 4.48/4.66 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 4.48/4.66 >>>> Starting back demodulation with 4.
% 4.48/4.66 >> back demodulating 1 with 4.
% 4.48/4.66 >>>> Starting back demodulation with 6.
% 4.48/4.66 >>>> Starting back demodulation with 8.
% 4.48/4.66 >>>> Starting back demodulation with 10.
% 4.48/4.66 >>>> Starting back demodulation with 12.
% 4.48/4.66
% 4.48/4.66 ======= end of input processing =======
% 4.48/4.66
% 4.48/4.66 =========== start of search ===========
% 4.48/4.66
% 4.48/4.66
% 4.48/4.66 Resetting weight limit to 12.
% 4.48/4.66
% 4.48/4.66
% 4.48/4.66 Resetting weight limit to 12.
% 4.48/4.66
% 4.48/4.66 sos_size=790
% 4.48/4.66
% 4.48/4.66 -------- PROOF --------
% 4.48/4.66
% 4.48/4.66 ----> UNIT CONFLICT at 2.66 sec ----> 1850 [binary,1849.1,2.1] $F.
% 4.48/4.66
% 4.48/4.66 Length of proof is 29. Level of proof is 10.
% 4.48/4.66
% 4.48/4.66 ---------------- PROOF ----------------
% 4.48/4.66 % SZS status Unsatisfiable
% 4.48/4.66 % SZS output start Refutation
% See solution above
% 4.48/4.66 ------------ end of proof -------------
% 4.48/4.66
% 4.48/4.66
% 4.48/4.66 Search stopped by max_proofs option.
% 4.48/4.66
% 4.48/4.66
% 4.48/4.66 Search stopped by max_proofs option.
% 4.48/4.66
% 4.48/4.66 ============ end of search ============
% 4.48/4.66
% 4.48/4.66 -------------- statistics -------------
% 4.48/4.66 clauses given 464
% 4.48/4.66 clauses generated 362145
% 4.48/4.66 clauses kept 1118
% 4.48/4.66 clauses forward subsumed 98660
% 4.48/4.66 clauses back subsumed 8
% 4.48/4.66 Kbytes malloced 5859
% 4.48/4.66
% 4.48/4.66 ----------- times (seconds) -----------
% 4.48/4.66 user CPU time 2.66 (0 hr, 0 min, 2 sec)
% 4.48/4.66 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 4.48/4.66 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 4.48/4.66
% 4.48/4.66 That finishes the proof of the theorem.
% 4.48/4.66
% 4.48/4.66 Process 30324 finished Wed Jul 27 02:33:39 2022
% 4.48/4.66 Otter interrupted
% 4.48/4.66 PROOF FOUND
%------------------------------------------------------------------------------