TSTP Solution File: GRP756-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP756-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 2.16s 2.31s
% Output : Refutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 5 RR)
% Number of literals : 34 ( 33 equ; 4 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(mult(a,b),c) != mult(a,mult(b,c)),
file('GRP756-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP756-1.p',unknown),
[] ).
cnf(4,axiom,
mult(A,ld(A,B)) = B,
file('GRP756-1.p',unknown),
[] ).
cnf(5,axiom,
ld(A,mult(A,B)) = B,
file('GRP756-1.p',unknown),
[] ).
cnf(7,axiom,
mult(rd(A,B),B) = A,
file('GRP756-1.p',unknown),
[] ).
cnf(9,axiom,
rd(mult(A,B),B) = A,
file('GRP756-1.p',unknown),
[] ).
cnf(11,axiom,
mult(A,mult(mult(B,B),C)) = mult(mult(A,B),mult(B,C)),
file('GRP756-1.p',unknown),
[] ).
cnf(12,plain,
mult(mult(A,B),mult(B,C)) = mult(A,mult(mult(B,B),C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(19,plain,
mult(mult(A,B),mult(B,ld(mult(B,B),C))) = mult(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,4])]),
[iquote('para_into,11.1.1.2,3.1.1,flip.1')] ).
cnf(27,plain,
ld(A,mult(mult(A,B),mult(B,C))) = mult(mult(B,B),C),
inference(para_from,[status(thm),theory(equality)],[11,5]),
[iquote('para_from,11.1.1,5.1.1.2')] ).
cnf(28,plain,
mult(mult(A,A),B) = ld(C,mult(mult(C,A),mult(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[27])]),
[iquote('copy,27,flip.1')] ).
cnf(38,plain,
mult(mult(A,B),C) = mult(A,mult(mult(B,B),ld(B,C))),
inference(para_into,[status(thm),theory(equality)],[12,4]),
[iquote('para_into,12.1.1.2,3.1.1')] ).
cnf(46,plain,
mult(A,mult(mult(B,B),ld(B,C))) = mult(mult(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[38])]),
[iquote('copy,38,flip.1')] ).
cnf(61,plain,
mult(rd(A,B),C) = mult(A,mult(B,ld(mult(B,B),C))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,7])]),
[iquote('para_into,19.1.1.1,7.1.1,flip.1')] ).
cnf(73,plain,
mult(A,mult(B,ld(mult(B,B),B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),61]),
[iquote('back_demod,7,demod,61')] ).
cnf(161,plain,
ld(A,A) = mult(B,ld(mult(B,B),B)),
inference(para_from,[status(thm),theory(equality)],[73,5]),
[iquote('para_from,73.1.1,5.1.1.2')] ).
cnf(173,plain,
mult(A,ld(mult(A,A),A)) = ld(B,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[161])]),
[iquote('copy,161,flip.1')] ).
cnf(313,plain,
mult(A,ld(B,B)) = A,
inference(para_from,[status(thm),theory(equality)],[173,73]),
[iquote('para_from,173.1.1,73.1.1.2')] ).
cnf(314,plain,
rd(ld(A,A),ld(mult(B,B),B)) = B,
inference(para_from,[status(thm),theory(equality)],[173,9]),
[iquote('para_from,173.1.1,9.1.1.1')] ).
cnf(316,plain,
ld(A,ld(B,B)) = ld(mult(A,A),A),
inference(para_from,[status(thm),theory(equality)],[173,5]),
[iquote('para_from,173.1.1,5.1.1.2')] ).
cnf(317,plain,
ld(mult(A,A),A) = ld(A,ld(B,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[316])]),
[iquote('copy,316,flip.1')] ).
cnf(328,plain,
rd(ld(A,A),ld(B,ld(C,C))) = B,
inference(para_from,[status(thm),theory(equality)],[317,314]),
[iquote('para_from,317.1.1,314.1.1.2')] ).
cnf(332,plain,
mult(mult(A,A),ld(A,ld(B,B))) = A,
inference(para_from,[status(thm),theory(equality)],[317,4]),
[iquote('para_from,317.1.1,3.1.1.2')] ).
cnf(388,plain,
ld(A,mult(mult(A,B),C)) = mult(mult(B,B),ld(B,C)),
inference(para_into,[status(thm),theory(equality)],[27,4]),
[iquote('para_into,27.1.1.2.2,3.1.1')] ).
cnf(389,plain,
mult(mult(A,A),ld(A,B)) = ld(C,mult(mult(C,A),B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[388])]),
[iquote('copy,388,flip.1')] ).
cnf(420,plain,
mult(a,mult(mult(b,b),ld(b,c))) != mult(a,mult(b,c)),
inference(para_from,[status(thm),theory(equality)],[38,1]),
[iquote('para_from,38.1.1,1.1.1')] ).
cnf(421,plain,
mult(A,ld(B,mult(mult(B,C),D))) = mult(mult(A,C),D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[46,28]),4]),
[iquote('para_into,46.1.1.2,28.1.1,demod,4')] ).
cnf(514,plain,
mult(a,ld(A,mult(mult(A,b),c))) != mult(a,mult(b,c)),
inference(para_into,[status(thm),theory(equality)],[420,389]),
[iquote('para_into,420.1.1.2,389.1.1')] ).
cnf(521,plain,
mult(mult(A,B),ld(B,ld(C,C))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[421,332]),313])]),
[iquote('para_into,421.1.1.2.2,332.1.1,demod,313,flip.1')] ).
cnf(547,plain,
rd(A,ld(B,ld(C,C))) = mult(A,B),
inference(para_from,[status(thm),theory(equality)],[521,9]),
[iquote('para_from,521.1.1,9.1.1.1')] ).
cnf(554,plain,
mult(ld(A,A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[328]),547]),
[iquote('back_demod,328,demod,547')] ).
cnf(563,plain,
ld(A,mult(mult(A,B),C)) = mult(B,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[554,421]),554])]),
[iquote('para_into,553.1.1,421.1.1,demod,554,flip.1')] ).
cnf(570,plain,
mult(a,mult(b,c)) != mult(a,mult(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[514]),563]),
[iquote('back_demod,514,demod,563')] ).
cnf(571,plain,
$false,
inference(binary,[status(thm)],[570,2]),
[iquote('binary,570.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP756-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:40:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.16/2.31 ----- Otter 3.3f, August 2004 -----
% 2.16/2.31 The process was started by sandbox on n026.cluster.edu,
% 2.16/2.31 Wed Jul 27 05:40:39 2022
% 2.16/2.31 The command was "./otter". The process ID is 23598.
% 2.16/2.31
% 2.16/2.31 set(prolog_style_variables).
% 2.16/2.31 set(auto).
% 2.16/2.31 dependent: set(auto1).
% 2.16/2.31 dependent: set(process_input).
% 2.16/2.31 dependent: clear(print_kept).
% 2.16/2.31 dependent: clear(print_new_demod).
% 2.16/2.31 dependent: clear(print_back_demod).
% 2.16/2.31 dependent: clear(print_back_sub).
% 2.16/2.31 dependent: set(control_memory).
% 2.16/2.31 dependent: assign(max_mem, 12000).
% 2.16/2.31 dependent: assign(pick_given_ratio, 4).
% 2.16/2.31 dependent: assign(stats_level, 1).
% 2.16/2.31 dependent: assign(max_seconds, 10800).
% 2.16/2.31 clear(print_given).
% 2.16/2.31
% 2.16/2.31 list(usable).
% 2.16/2.31 0 [] A=A.
% 2.16/2.31 0 [] mult(A,ld(A,B))=B.
% 2.16/2.31 0 [] ld(A,mult(A,B))=B.
% 2.16/2.31 0 [] mult(rd(A,B),B)=A.
% 2.16/2.31 0 [] rd(mult(A,B),B)=A.
% 2.16/2.31 0 [] mult(A,mult(mult(B,B),C))=mult(mult(A,B),mult(B,C)).
% 2.16/2.31 0 [] mult(mult(a,b),c)!=mult(a,mult(b,c)).
% 2.16/2.31 end_of_list.
% 2.16/2.31
% 2.16/2.31 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.16/2.31
% 2.16/2.31 All clauses are units, and equality is present; the
% 2.16/2.31 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.16/2.31
% 2.16/2.31 dependent: set(knuth_bendix).
% 2.16/2.31 dependent: set(anl_eq).
% 2.16/2.31 dependent: set(para_from).
% 2.16/2.31 dependent: set(para_into).
% 2.16/2.31 dependent: clear(para_from_right).
% 2.16/2.31 dependent: clear(para_into_right).
% 2.16/2.31 dependent: set(para_from_vars).
% 2.16/2.31 dependent: set(eq_units_both_ways).
% 2.16/2.31 dependent: set(dynamic_demod_all).
% 2.16/2.31 dependent: set(dynamic_demod).
% 2.16/2.31 dependent: set(order_eq).
% 2.16/2.31 dependent: set(back_demod).
% 2.16/2.31 dependent: set(lrpo).
% 2.16/2.31
% 2.16/2.31 ------------> process usable:
% 2.16/2.31 ** KEPT (pick-wt=11): 1 [] mult(mult(a,b),c)!=mult(a,mult(b,c)).
% 2.16/2.31
% 2.16/2.31 ------------> process sos:
% 2.16/2.31 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.16/2.31 ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 2.16/2.31 ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 2.16/2.31 ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 2.16/2.31 ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 2.16/2.31 ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 2.16/2.31 ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 2.16/2.31 ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 2.16/2.31 ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 2.16/2.31 ** KEPT (pick-wt=15): 11 [] mult(A,mult(mult(B,B),C))=mult(mult(A,B),mult(B,C)).
% 2.16/2.31 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.16/2.31 >>>> Starting back demodulation with 4.
% 2.16/2.31 >>>> Starting back demodulation with 6.
% 2.16/2.31 >>>> Starting back demodulation with 8.
% 2.16/2.31 >>>> Starting back demodulation with 10.
% 2.16/2.31 ** KEPT (pick-wt=15): 12 [copy,11,flip.1] mult(mult(A,B),mult(B,C))=mult(A,mult(mult(B,B),C)).
% 2.16/2.31 Following clause subsumed by 11 during input processing: 0 [copy,12,flip.1] mult(A,mult(mult(B,B),C))=mult(mult(A,B),mult(B,C)).
% 2.16/2.31
% 2.16/2.31 ======= end of input processing =======
% 2.16/2.31
% 2.16/2.31 =========== start of search ===========
% 2.16/2.31
% 2.16/2.31
% 2.16/2.31 Resetting weight limit to 15.
% 2.16/2.31
% 2.16/2.31
% 2.16/2.31 Resetting weight limit to 15.
% 2.16/2.31
% 2.16/2.31 sos_size=193
% 2.16/2.31
% 2.16/2.31 -------- PROOF --------
% 2.16/2.31
% 2.16/2.31 ----> UNIT CONFLICT at 0.22 sec ----> 571 [binary,570.1,2.1] $F.
% 2.16/2.31
% 2.16/2.31 Length of proof is 26. Level of proof is 13.
% 2.16/2.31
% 2.16/2.31 ---------------- PROOF ----------------
% 2.16/2.31 % SZS status Unsatisfiable
% 2.16/2.31 % SZS output start Refutation
% See solution above
% 2.16/2.31 ------------ end of proof -------------
% 2.16/2.31
% 2.16/2.31
% 2.16/2.31 Search stopped by max_proofs option.
% 2.16/2.31
% 2.16/2.31
% 2.16/2.31 Search stopped by max_proofs option.
% 2.16/2.31
% 2.16/2.31 ============ end of search ============
% 2.16/2.31
% 2.16/2.31 -------------- statistics -------------
% 2.16/2.31 clauses given 130
% 2.16/2.31 clauses generated 13721
% 2.16/2.31 clauses kept 407
% 2.16/2.31 clauses forward subsumed 4665
% 2.16/2.31 clauses back subsumed 8
% 2.16/2.31 Kbytes malloced 6835
% 2.16/2.31
% 2.16/2.31 ----------- times (seconds) -----------
% 2.16/2.31 user CPU time 0.22 (0 hr, 0 min, 0 sec)
% 2.16/2.31 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.16/2.31 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.16/2.31
% 2.16/2.31 That finishes the proof of the theorem.
% 2.16/2.31
% 2.16/2.31 Process 23598 finished Wed Jul 27 05:40:41 2022
% 2.16/2.31 Otter interrupted
% 2.16/2.31 PROOF FOUND
%------------------------------------------------------------------------------