TSTP Solution File: GRP750-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP750-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:57:46 EDT 2022
% Result : Unsatisfiable 2.34s 2.57s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 3 RR)
% Number of literals : 44 ( 43 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 119 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
file('GRP750-1.p',unknown),
[] ).
cnf(2,plain,
mult(mult(a,b),mult(a,c)) != mult(mult(a,a),mult(b,c)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
mult(A,ld(A,B)) = B,
file('GRP750-1.p',unknown),
[] ).
cnf(7,axiom,
ld(A,mult(A,B)) = B,
file('GRP750-1.p',unknown),
[] ).
cnf(9,axiom,
mult(rd(A,B),B) = A,
file('GRP750-1.p',unknown),
[] ).
cnf(11,axiom,
rd(mult(A,B),B) = A,
file('GRP750-1.p',unknown),
[] ).
cnf(12,axiom,
mult(mult(A,mult(A,A)),mult(B,C)) = mult(mult(A,B),mult(mult(A,A),C)),
file('GRP750-1.p',unknown),
[] ).
cnf(13,axiom,
mult(mult(A,B),mult(C,C)) = mult(mult(A,C),mult(B,C)),
file('GRP750-1.p',unknown),
[] ).
cnf(15,plain,
mult(mult(A,B),mult(C,B)) = mult(mult(A,C),mult(B,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(36,plain,
mult(mult(rd(A,B),C),mult(B,C)) = mult(A,mult(C,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,9])]),
[iquote('para_into,13.1.1.1,8.1.1,flip.1')] ).
cnf(46,plain,
rd(mult(mult(A,B),mult(C,B)),mult(B,B)) = mult(A,C),
inference(para_from,[status(thm),theory(equality)],[13,11]),
[iquote('para_from,13.1.1,10.1.1.1')] ).
cnf(48,plain,
ld(mult(A,B),mult(mult(A,C),mult(B,C))) = mult(C,C),
inference(para_from,[status(thm),theory(equality)],[13,7]),
[iquote('para_from,13.1.1,6.1.1.2')] ).
cnf(56,plain,
mult(mult(rd(A,B),C),mult(B,B)) = mult(A,mult(C,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,9])]),
[iquote('para_into,15.1.1.1,8.1.1,flip.1')] ).
cnf(57,plain,
mult(A,mult(B,ld(C,A))) = mult(mult(C,B),mult(ld(C,A),ld(C,A))),
inference(para_into,[status(thm),theory(equality)],[15,4]),
[iquote('para_into,15.1.1.1,4.1.1')] ).
cnf(78,plain,
ld(mult(A,B),mult(mult(A,C),mult(B,B))) = mult(C,B),
inference(para_from,[status(thm),theory(equality)],[15,7]),
[iquote('para_from,15.1.1,6.1.1.2')] ).
cnf(130,plain,
mult(mult(rd(A,rd(B,C)),C),B) = mult(A,mult(C,C)),
inference(para_into,[status(thm),theory(equality)],[36,9]),
[iquote('para_into,36.1.1.2,8.1.1')] ).
cnf(142,plain,
rd(mult(A,mult(B,B)),mult(C,B)) = mult(rd(A,C),B),
inference(para_from,[status(thm),theory(equality)],[36,11]),
[iquote('para_from,36.1.1,10.1.1.1')] ).
cnf(231,plain,
rd(mult(A,mult(B,C)),mult(C,C)) = mult(rd(A,C),B),
inference(para_into,[status(thm),theory(equality)],[46,9]),
[iquote('para_into,46.1.1.1.1,8.1.1')] ).
cnf(359,plain,
ld(mult(rd(A,B),C),mult(A,mult(C,B))) = mult(B,B),
inference(para_into,[status(thm),theory(equality)],[48,9]),
[iquote('para_into,48.1.1.2.1,8.1.1')] ).
cnf(463,plain,
ld(A,mult(mult(B,C),mult(ld(B,A),ld(B,A)))) = mult(C,ld(B,A)),
inference(para_into,[status(thm),theory(equality)],[78,4]),
[iquote('para_into,78.1.1.1,4.1.1')] ).
cnf(569,plain,
rd(mult(A,mult(B,B)),C) = mult(rd(A,rd(C,B)),B),
inference(para_from,[status(thm),theory(equality)],[130,11]),
[iquote('para_from,130.1.1,10.1.1.1')] ).
cnf(570,plain,
mult(rd(A,rd(B,C)),C) = rd(mult(A,mult(C,C)),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[569])]),
[iquote('copy,569,flip.1')] ).
cnf(572,plain,
rd(mult(A,mult(B,C)),mult(D,C)) = mult(rd(mult(rd(A,C),B),D),C),
inference(para_into,[status(thm),theory(equality)],[142,56]),
[iquote('para_into,142.1.1.1,55.1.1')] ).
cnf(620,plain,
rd(mult(A,B),mult(C,C)) = mult(rd(A,C),rd(B,C)),
inference(para_into,[status(thm),theory(equality)],[231,9]),
[iquote('para_into,231.1.1.1.2,8.1.1')] ).
cnf(622,plain,
mult(rd(mult(A,B),C),mult(A,A)) = mult(rd(mult(A,mult(A,A)),C),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[231,12]),620,11]),
[iquote('para_into,231.1.1.1,12.1.1,demod,620,11')] ).
cnf(653,plain,
rd(rd(mult(A,mult(B,B)),C),B) = rd(A,rd(C,B)),
inference(para_from,[status(thm),theory(equality)],[570,11]),
[iquote('para_from,570.1.1,10.1.1.1')] ).
cnf(708,plain,
rd(rd(mult(A,mult(B,C)),D),C) = rd(mult(rd(A,C),B),rd(D,C)),
inference(para_into,[status(thm),theory(equality)],[653,56]),
[iquote('para_into,653.1.1.1.1,55.1.1')] ).
cnf(783,plain,
mult(mult(A,A),mult(ld(A,B),ld(A,B))) = mult(B,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,4])]),
[iquote('para_into,57.1.1.2,4.1.1,flip.1')] ).
cnf(792,plain,
mult(ld(A,B),ld(A,B)) = ld(mult(A,A),mult(B,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[783,359]),9])]),
[iquote('para_from,783.1.1,359.1.1.2,demod,9,flip.1')] ).
cnf(822,plain,
ld(A,mult(mult(B,C),ld(mult(B,B),mult(A,A)))) = mult(C,ld(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[463]),792]),
[iquote('back_demod,463,demod,792')] ).
cnf(891,plain,
mult(rd(A,rd(B,A)),rd(C,A)) = rd(mult(A,C),B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[622,11]),620,708,9]),
[iquote('para_from,622.1.1,10.1.1.1,demod,620,708,9')] ).
cnf(893,plain,
rd(mult(A,B),mult(C,A)) = mult(rd(A,C),rd(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[891,11])]),
[iquote('para_into,891.1.1.1.2,10.1.1,flip.1')] ).
cnf(928,plain,
mult(rd(mult(rd(A,A),B),C),A) = mult(rd(A,C),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[893,572]),11]),
[iquote('para_into,893.1.1,572.1.1,demod,11')] ).
cnf(1011,plain,
mult(mult(rd(A,A),B),mult(A,C)) = mult(A,mult(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[928,56]),56])]),
[iquote('para_from,928.1.1,55.1.1.1,demod,56,flip.1')] ).
cnf(1140,plain,
mult(mult(rd(A,A),B),C) = mult(A,mult(B,ld(A,C))),
inference(para_into,[status(thm),theory(equality)],[1011,4]),
[iquote('para_into,1011.1.1.2,4.1.1')] ).
cnf(1222,plain,
mult(A,mult(B,ld(A,ld(mult(rd(A,A),B),C)))) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1140,4])]),
[iquote('para_into,1139.1.1,4.1.1,flip.1')] ).
cnf(1278,plain,
mult(A,ld(B,ld(mult(rd(B,B),A),C))) = ld(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1222,7])]),
[iquote('para_from,1222.1.1,6.1.1.2,flip.1')] ).
cnf(1320,plain,
mult(A,ld(B,mult(C,A))) = mult(C,ld(B,mult(A,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1278,78]),1140,7]),
[iquote('para_into,1278.1.1.2.2,78.1.1,demod,1140,7')] ).
cnf(1337,plain,
ld(A,mult(B,ld(C,mult(A,A)))) = ld(C,mult(B,A)),
inference(para_from,[status(thm),theory(equality)],[1320,7]),
[iquote('para_from,1320.1.1,6.1.1.2')] ).
cnf(1338,plain,
ld(mult(A,A),mult(mult(A,B),C)) = mult(B,ld(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[822]),1337]),
[iquote('back_demod,822,demod,1337')] ).
cnf(1366,plain,
mult(mult(A,A),mult(B,ld(A,C))) = mult(mult(A,B),C),
inference(para_from,[status(thm),theory(equality)],[1338,4]),
[iquote('para_from,1338.1.1,4.1.1.2')] ).
cnf(1392,plain,
mult(mult(A,A),mult(B,C)) = mult(mult(A,B),mult(A,C)),
inference(para_into,[status(thm),theory(equality)],[1366,7]),
[iquote('para_into,1366.1.1.2.2,6.1.1')] ).
cnf(1397,plain,
mult(mult(A,B),mult(A,C)) = mult(mult(A,A),mult(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1392])]),
[iquote('copy,1392,flip.1')] ).
cnf(1398,plain,
$false,
inference(binary,[status(thm)],[1397,2]),
[iquote('binary,1397.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP750-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 05:20:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.34/2.56 ----- Otter 3.3f, August 2004 -----
% 2.34/2.56 The process was started by sandbox2 on n014.cluster.edu,
% 2.34/2.56 Wed Jul 27 05:20:24 2022
% 2.34/2.56 The command was "./otter". The process ID is 3949.
% 2.34/2.56
% 2.34/2.56 set(prolog_style_variables).
% 2.34/2.56 set(auto).
% 2.34/2.56 dependent: set(auto1).
% 2.34/2.56 dependent: set(process_input).
% 2.34/2.56 dependent: clear(print_kept).
% 2.34/2.56 dependent: clear(print_new_demod).
% 2.34/2.56 dependent: clear(print_back_demod).
% 2.34/2.56 dependent: clear(print_back_sub).
% 2.34/2.56 dependent: set(control_memory).
% 2.34/2.56 dependent: assign(max_mem, 12000).
% 2.34/2.56 dependent: assign(pick_given_ratio, 4).
% 2.34/2.56 dependent: assign(stats_level, 1).
% 2.34/2.56 dependent: assign(max_seconds, 10800).
% 2.34/2.56 clear(print_given).
% 2.34/2.56
% 2.34/2.56 list(usable).
% 2.34/2.56 0 [] A=A.
% 2.34/2.56 0 [] mult(A,ld(A,B))=B.
% 2.34/2.56 0 [] ld(A,mult(A,B))=B.
% 2.34/2.56 0 [] mult(rd(A,B),B)=A.
% 2.34/2.56 0 [] rd(mult(A,B),B)=A.
% 2.34/2.56 0 [] mult(mult(A,mult(A,A)),mult(B,C))=mult(mult(A,B),mult(mult(A,A),C)).
% 2.34/2.56 0 [] mult(mult(A,B),mult(C,C))=mult(mult(A,C),mult(B,C)).
% 2.34/2.56 0 [] mult(mult(a,a),mult(b,c))!=mult(mult(a,b),mult(a,c)).
% 2.34/2.56 end_of_list.
% 2.34/2.56
% 2.34/2.56 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.34/2.57
% 2.34/2.57 All clauses are units, and equality is present; the
% 2.34/2.57 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.34/2.57
% 2.34/2.57 dependent: set(knuth_bendix).
% 2.34/2.57 dependent: set(anl_eq).
% 2.34/2.57 dependent: set(para_from).
% 2.34/2.57 dependent: set(para_into).
% 2.34/2.57 dependent: clear(para_from_right).
% 2.34/2.57 dependent: clear(para_into_right).
% 2.34/2.57 dependent: set(para_from_vars).
% 2.34/2.57 dependent: set(eq_units_both_ways).
% 2.34/2.57 dependent: set(dynamic_demod_all).
% 2.34/2.57 dependent: set(dynamic_demod).
% 2.34/2.57 dependent: set(order_eq).
% 2.34/2.57 dependent: set(back_demod).
% 2.34/2.57 dependent: set(lrpo).
% 2.34/2.57
% 2.34/2.57 ------------> process usable:
% 2.34/2.57 ** KEPT (pick-wt=15): 2 [copy,1,flip.1] mult(mult(a,b),mult(a,c))!=mult(mult(a,a),mult(b,c)).
% 2.34/2.57
% 2.34/2.57 ------------> process sos:
% 2.34/2.57 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.34/2.57 ** KEPT (pick-wt=7): 4 [] mult(A,ld(A,B))=B.
% 2.34/2.57 ---> New Demodulator: 5 [new_demod,4] mult(A,ld(A,B))=B.
% 2.34/2.57 ** KEPT (pick-wt=7): 6 [] ld(A,mult(A,B))=B.
% 2.34/2.57 ---> New Demodulator: 7 [new_demod,6] ld(A,mult(A,B))=B.
% 2.34/2.57 ** KEPT (pick-wt=7): 8 [] mult(rd(A,B),B)=A.
% 2.34/2.57 ---> New Demodulator: 9 [new_demod,8] mult(rd(A,B),B)=A.
% 2.34/2.57 ** KEPT (pick-wt=7): 10 [] rd(mult(A,B),B)=A.
% 2.34/2.57 ---> New Demodulator: 11 [new_demod,10] rd(mult(A,B),B)=A.
% 2.34/2.57 ** KEPT (pick-wt=19): 12 [] mult(mult(A,mult(A,A)),mult(B,C))=mult(mult(A,B),mult(mult(A,A),C)).
% 2.34/2.57 ** KEPT (pick-wt=15): 13 [] mult(mult(A,B),mult(C,C))=mult(mult(A,C),mult(B,C)).
% 2.34/2.57 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.34/2.57 >>>> Starting back demodulation with 5.
% 2.34/2.57 >>>> Starting back demodulation with 7.
% 2.34/2.57 >>>> Starting back demodulation with 9.
% 2.34/2.57 >>>> Starting back demodulation with 11.
% 2.34/2.57 ** KEPT (pick-wt=19): 14 [copy,12,flip.1] mult(mult(A,B),mult(mult(A,A),C))=mult(mult(A,mult(A,A)),mult(B,C)).
% 2.34/2.57 ** KEPT (pick-wt=15): 15 [copy,13,flip.1] mult(mult(A,B),mult(C,B))=mult(mult(A,C),mult(B,B)).
% 2.34/2.57 Following clause subsumed by 12 during input processing: 0 [copy,14,flip.1] mult(mult(A,mult(A,A)),mult(B,C))=mult(mult(A,B),mult(mult(A,A),C)).
% 2.34/2.57 Following clause subsumed by 13 during input processing: 0 [copy,15,flip.1] mult(mult(A,B),mult(C,C))=mult(mult(A,C),mult(B,C)).
% 2.34/2.57
% 2.34/2.57 ======= end of input processing =======
% 2.34/2.57
% 2.34/2.57 =========== start of search ===========
% 2.34/2.57
% 2.34/2.57
% 2.34/2.57 Resetting weight limit to 19.
% 2.34/2.57
% 2.34/2.57
% 2.34/2.57 Resetting weight limit to 19.
% 2.34/2.57
% 2.34/2.57 sos_size=363
% 2.34/2.57
% 2.34/2.57
% 2.34/2.57 Resetting weight limit to 15.
% 2.34/2.57
% 2.34/2.57
% 2.34/2.57 Resetting weight limit to 15.
% 2.34/2.57
% 2.34/2.57 sos_size=435
% 2.34/2.57
% 2.34/2.57 -------- PROOF --------
% 2.34/2.57
% 2.34/2.57 ----> UNIT CONFLICT at 0.69 sec ----> 1398 [binary,1397.1,2.1] $F.
% 2.34/2.57
% 2.34/2.57 Length of proof is 36. Level of proof is 19.
% 2.34/2.57
% 2.34/2.57 ---------------- PROOF ----------------
% 2.34/2.57 % SZS status Unsatisfiable
% 2.34/2.57 % SZS output start Refutation
% See solution above
% 2.34/2.57 ------------ end of proof -------------
% 2.34/2.57
% 2.34/2.57
% 2.34/2.57 Search stopped by max_proofs option.
% 2.34/2.57
% 2.34/2.57
% 2.34/2.57 Search stopped by max_proofs option.
% 2.34/2.57
% 2.34/2.57 ============ end of search ============
% 2.34/2.57
% 2.34/2.57 -------------- statistics -------------
% 2.34/2.57 clauses given 305
% 2.34/2.57 clauses generated 72933
% 2.34/2.57 clauses kept 967
% 2.34/2.57 clauses forward subsumed 5470
% 2.34/2.57 clauses back subsumed 26
% 2.34/2.57 Kbytes malloced 8789
% 2.34/2.57
% 2.34/2.57 ----------- times (seconds) -----------
% 2.34/2.57 user CPU time 0.69 (0 hr, 0 min, 0 sec)
% 2.34/2.57 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.34/2.57 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.34/2.57
% 2.34/2.57 That finishes the proof of the theorem.
% 2.34/2.57
% 2.34/2.57 Process 3949 finished Wed Jul 27 05:20:26 2022
% 2.34/2.57 Otter interrupted
% 2.34/2.57 PROOF FOUND
%------------------------------------------------------------------------------