%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP703-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 12:57:41 EDT 2022
% Result : Unsatisfiable 1.68s 1.89s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 6 RR)
% Number of literals : 21 ( 20 equ; 3 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; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(x2,mult(x3,op_e)) != mult(mult(x2,x3),op_e),
file('GRP703-11.p',unknown),
[] ).
cnf(2,plain,
mult(mult(x2,x3),op_e) != mult(x2,mult(x3,op_e)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
A = A,
file('GRP703-11.p',unknown),
[] ).
cnf(4,axiom,
mult(A,ld(A,B)) = B,
file('GRP703-11.p',unknown),
[] ).
cnf(9,axiom,
mult(rd(A,B),B) = A,
file('GRP703-11.p',unknown),
[] ).
cnf(12,axiom,
mult(A,unit) = A,
file('GRP703-11.p',unknown),
[] ).
cnf(14,axiom,
mult(unit,A) = A,
file('GRP703-11.p',unknown),
[] ).
cnf(22,axiom,
mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
file('GRP703-11.p',unknown),
[] ).
cnf(24,plain,
mult(mult(A,B),op_c) = mult(A,mult(B,op_c)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
[iquote('copy,22,flip.1')] ).
cnf(28,axiom,
op_d = ld(A,mult(op_c,A)),
file('GRP703-11.p',unknown),
[] ).
cnf(29,plain,
ld(A,mult(op_c,A)) = op_d,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[28])]),
[iquote('copy,28,flip.1')] ).
cnf(31,axiom,
op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
file('GRP703-11.p',unknown),
[] ).
cnf(32,plain,
mult(mult(rd(op_c,mult(A,B)),B),A) = op_e,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[31])]),
[iquote('copy,31,flip.1')] ).
cnf(38,plain,
ld(unit,A) = A,
inference(para_into,[status(thm),theory(equality)],[4,14]),
[iquote('para_into,4.1.1,14.1.1')] ).
cnf(66,plain,
op_d = op_c,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,12]),38])]),
[iquote('para_into,29.1.1.2,12.1.1,demod,38,flip.1')] ).
cnf(69,plain,
ld(A,mult(op_c,A)) = op_c,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),66]),
[iquote('back_demod,29,demod,66')] ).
cnf(83,plain,
mult(A,op_c) = mult(op_c,A),
inference(para_from,[status(thm),theory(equality)],[69,4]),
[iquote('para_from,69.1.1,4.1.1.2')] ).
cnf(84,plain,
mult(op_c,A) = mult(A,op_c),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[83])]),
[iquote('copy,83,flip.1')] ).
cnf(120,plain,
op_e = op_c,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,84]),24,9])]),
[iquote('para_into,32.1.1.1.1.2,84.1.1,demod,24,9,flip.1')] ).
cnf(141,plain,
mult(x2,mult(x3,op_c)) != mult(x2,mult(x3,op_c)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),120,24,120]),
[iquote('back_demod,2,demod,120,24,120')] ).
cnf(142,plain,
$false,
inference(binary,[status(thm)],[141,3]),
[iquote('binary,141.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP703-11 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 05:14:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox2 on n007.cluster.edu,
% 1.68/1.89 Wed Jul 27 05:14:01 2022
% 1.68/1.89 The command was "./otter". The process ID is 13287.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] A=A.
% 1.68/1.89 0 [] mult(A,ld(A,B))=B.
% 1.68/1.89 0 [] ld(A,mult(A,B))=B.
% 1.68/1.89 0 [] mult(rd(A,B),B)=A.
% 1.68/1.89 0 [] rd(mult(A,B),B)=A.
% 1.68/1.89 0 [] mult(A,unit)=A.
% 1.68/1.89 0 [] mult(unit,A)=A.
% 1.68/1.89 0 [] mult(A,mult(B,mult(B,C)))=mult(mult(mult(A,B),B),C).
% 1.68/1.89 0 [] mult(op_c,mult(A,B))=mult(mult(op_c,A),B).
% 1.68/1.89 0 [] mult(A,mult(B,op_c))=mult(mult(A,B),op_c).
% 1.68/1.89 0 [] mult(A,mult(op_c,B))=mult(mult(A,op_c),B).
% 1.68/1.89 0 [] op_d=ld(A,mult(op_c,A)).
% 1.68/1.89 0 [] op_e=mult(mult(rd(op_c,mult(A,B)),B),A).
% 1.68/1.89 0 [] op_f=mult(A,mult(B,ld(mult(A,B),op_c))).
% 1.68/1.89 0 [] mult(x2,mult(x3,op_e))!=mult(mult(x2,x3),op_e).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.89
% 1.68/1.89 All clauses are units, and equality is present; the
% 1.68/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.89
% 1.68/1.89 dependent: set(knuth_bendix).
% 1.68/1.89 dependent: set(anl_eq).
% 1.68/1.89 dependent: set(para_from).
% 1.68/1.89 dependent: set(para_into).
% 1.68/1.89 dependent: clear(para_from_right).
% 1.68/1.89 dependent: clear(para_into_right).
% 1.68/1.89 dependent: set(para_from_vars).
% 1.68/1.89 dependent: set(eq_units_both_ways).
% 1.68/1.89 dependent: set(dynamic_demod_all).
% 1.68/1.89 dependent: set(dynamic_demod).
% 1.68/1.89 dependent: set(order_eq).
% 1.68/1.89 dependent: set(back_demod).
% 1.68/1.89 dependent: set(lrpo).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=11): 2 [copy,1,flip.1] mult(mult(x2,x3),op_e)!=mult(x2,mult(x3,op_e)).
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.68/1.89 ** KEPT (pick-wt=7): 4 [] mult(A,ld(A,B))=B.
% 1.68/1.89 ---> New Demodulator: 5 [new_demod,4] mult(A,ld(A,B))=B.
% 1.68/1.89 ** KEPT (pick-wt=7): 6 [] ld(A,mult(A,B))=B.
% 1.68/1.89 ---> New Demodulator: 7 [new_demod,6] ld(A,mult(A,B))=B.
% 1.68/1.89 ** KEPT (pick-wt=7): 8 [] mult(rd(A,B),B)=A.
% 1.68/1.89 ---> New Demodulator: 9 [new_demod,8] mult(rd(A,B),B)=A.
% 1.68/1.89 ** KEPT (pick-wt=7): 10 [] rd(mult(A,B),B)=A.
% 1.68/1.89 ---> New Demodulator: 11 [new_demod,10] rd(mult(A,B),B)=A.
% 1.68/1.89 ** KEPT (pick-wt=5): 12 [] mult(A,unit)=A.
% 1.68/1.89 ---> New Demodulator: 13 [new_demod,12] mult(A,unit)=A.
% 1.68/1.89 ** KEPT (pick-wt=5): 14 [] mult(unit,A)=A.
% 1.68/1.89 ---> New Demodulator: 15 [new_demod,14] mult(unit,A)=A.
% 1.68/1.89 ** KEPT (pick-wt=15): 17 [copy,16,flip.1] mult(mult(mult(A,B),B),C)=mult(A,mult(B,mult(B,C))).
% 1.68/1.89 ---> New Demodulator: 18 [new_demod,17] mult(mult(mult(A,B),B),C)=mult(A,mult(B,mult(B,C))).
% 1.68/1.89 ** KEPT (pick-wt=11): 20 [copy,19,flip.1] mult(mult(op_c,A),B)=mult(op_c,mult(A,B)).
% 1.68/1.89 ---> New Demodulator: 21 [new_demod,20] mult(mult(op_c,A),B)=mult(op_c,mult(A,B)).
% 1.68/1.89 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] mult(mult(A,B),op_c)=mult(A,mult(B,op_c)).
% 1.68/1.89 ---> New Demodulator: 24 [new_demod,23] mult(mult(A,B),op_c)=mult(A,mult(B,op_c)).
% 1.68/1.89 ** KEPT (pick-wt=11): 26 [copy,25,flip.1] mult(mult(A,op_c),B)=mult(A,mult(op_c,B)).
% 1.68/1.89 ---> New Demodulator: 27 [new_demod,26] mult(mult(A,op_c),B)=mult(A,mult(op_c,B)).
% 1.68/1.89 ** KEPT (pick-wt=7): 29 [copy,28,flip.1] ld(A,mult(op_c,A))=op_d.
% 1.68/1.89 ---> New Demodulator: 30 [new_demod,29] ld(A,mult(op_c,A))=op_d.
% 1.68/1.89 ** KEPT (pick-wt=11): 32 [copy,31,flip.1] mult(mult(rd(op_c,mult(A,B)),B),A)=op_e.
% 1.68/1.89 ---> New Demodulator: 33 [new_demod,32] mult(mult(rd(op_c,mult(A,B)),B),A)=op_e.
% 1.68/1.89 ** KEPT (pick-wt=11): 35 [copy,34,flip.1] mult(A,mult(B,ld(mult(A,B),op_c)))=op_f.
% 1.68/1.89 ---> New Demodulator: 36 [new_demod,35] mult(A,mult(B,ld(mult(A,B),op_c)))=op_f.
% 1.68/1.89 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.68/1.89 >>>> Starting back demodulation with 5.
% 1.68/1.89 >>>> Starting back demodulation with 7.
% 1.68/1.89 >>>> Starting back demodulation with 9.
% 1.68/1.89 >>>> Starting back demodulation with 11.
% 1.68/1.89 >>>> Starting back demodulation with 13.
% 1.68/1.89 >>>> Starting back demodulation with 15.
% 1.68/1.89 >>>> Starting back demodulation with 18.
% 1.68/1.89 >>>> Starting back demodulation with 21.
% 1.68/1.89 >>>> Starting back demodulation with 24.
% 1.68/1.89 >>>> Starting back demodulation with 27.
% 1.68/1.89 >>>> Starting back demodulation with 30.
% 1.68/1.89 >>>> Starting back demodulation with 33.
% 1.68/1.89 >>>> Starting back demodulation with 36.
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 142 [binary,141.1,3.1] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 11. Level of proof is 7.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Unsatisfiable
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 28
% 1.68/1.89 clauses generated 243
% 1.68/1.89 clauses kept 71
% 1.68/1.89 clauses forward subsumed 200
% 1.68/1.89 clauses back subsumed 0
% 1.68/1.89 Kbytes malloced 1953
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 13287 finished Wed Jul 27 05:14:02 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------