%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP665-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:57:36 EDT 2022
% Result : Unsatisfiable 1.67s 1.89s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 4 RR)
% Number of literals : 15 ( 14 equ; 3 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c)),
file('GRP665-12.p',unknown),
[] ).
cnf(3,axiom,
mult(A,ld(A,B)) = B,
file('GRP665-12.p',unknown),
[] ).
cnf(6,axiom,
ld(A,mult(A,B)) = B,
file('GRP665-12.p',unknown),
[] ).
cnf(9,axiom,
rd(mult(A,B),B) = A,
file('GRP665-12.p',unknown),
[] ).
cnf(15,axiom,
mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
file('GRP665-12.p',unknown),
[] ).
cnf(16,plain,
mult(rd(mult(A,B),A),mult(A,C)) = mult(A,mult(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(19,axiom,
mult(op_c,A) = mult(A,op_c),
file('GRP665-12.p',unknown),
[] ).
cnf(21,plain,
mult(A,op_c) = mult(op_c,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(38,plain,
mult(rd(A,B),mult(B,C)) = mult(B,mult(ld(B,A),C)),
inference(para_into,[status(thm),theory(equality)],[16,3]),
[iquote('para_into,16.1.1.1.1,3.1.1')] ).
cnf(52,plain,
rd(mult(A,op_c),A) = op_c,
inference(para_from,[status(thm),theory(equality)],[19,9]),
[iquote('para_from,19.1.1,9.1.1.1')] ).
cnf(62,plain,
mult(x0,mult(x1,op_c)) != mult(op_c,mult(x0,x1)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[21,1])]),
[iquote('para_from,21.1.1,1.1.1,flip.1')] ).
cnf(112,plain,
mult(x0,mult(op_c,x1)) != mult(op_c,mult(x0,x1)),
inference(para_into,[status(thm),theory(equality)],[62,21]),
[iquote('para_into,62.1.1.2,21.1.1')] ).
cnf(115,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[38,52]),6]),
[iquote('para_into,38.1.1.1,52.1.1,demod,6')] ).
cnf(136,plain,
mult(A,mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[115])]),
[iquote('copy,115,flip.1')] ).
cnf(137,plain,
$false,
inference(binary,[status(thm)],[136,112]),
[iquote('binary,136.1,112.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP665-12 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 05:13:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox2 on n012.cluster.edu,
% 1.67/1.89 Wed Jul 27 05:13:05 2022
% 1.67/1.89 The command was "./otter". The process ID is 6019.
% 1.67/1.89
% 1.67/1.89 set(prolog_style_variables).
% 1.67/1.89 set(auto).
% 1.67/1.89 dependent: set(auto1).
% 1.67/1.89 dependent: set(process_input).
% 1.67/1.89 dependent: clear(print_kept).
% 1.67/1.89 dependent: clear(print_new_demod).
% 1.67/1.89 dependent: clear(print_back_demod).
% 1.67/1.89 dependent: clear(print_back_sub).
% 1.67/1.89 dependent: set(control_memory).
% 1.67/1.89 dependent: assign(max_mem, 12000).
% 1.67/1.89 dependent: assign(pick_given_ratio, 4).
% 1.67/1.89 dependent: assign(stats_level, 1).
% 1.67/1.89 dependent: assign(max_seconds, 10800).
% 1.67/1.89 clear(print_given).
% 1.67/1.89
% 1.67/1.89 list(usable).
% 1.67/1.89 0 [] A=A.
% 1.67/1.89 0 [] mult(A,ld(A,B))=B.
% 1.67/1.89 0 [] ld(A,mult(A,B))=B.
% 1.67/1.89 0 [] mult(rd(A,B),B)=A.
% 1.67/1.89 0 [] rd(mult(A,B),B)=A.
% 1.67/1.89 0 [] mult(A,unit)=A.
% 1.67/1.89 0 [] mult(unit,A)=A.
% 1.67/1.89 0 [] mult(A,mult(B,C))=mult(rd(mult(A,B),A),mult(A,C)).
% 1.67/1.89 0 [] mult(mult(A,B),C)=mult(mult(A,C),ld(C,mult(B,C))).
% 1.67/1.89 0 [] mult(op_c,A)=mult(A,op_c).
% 1.67/1.89 0 [] mult(mult(x0,x1),op_c)!=mult(x0,mult(x1,op_c)).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.67/1.89
% 1.67/1.89 All clauses are units, and equality is present; the
% 1.67/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.67/1.89
% 1.67/1.89 dependent: set(knuth_bendix).
% 1.67/1.89 dependent: set(anl_eq).
% 1.67/1.89 dependent: set(para_from).
% 1.67/1.89 dependent: set(para_into).
% 1.67/1.89 dependent: clear(para_from_right).
% 1.67/1.89 dependent: clear(para_into_right).
% 1.67/1.89 dependent: set(para_from_vars).
% 1.67/1.89 dependent: set(eq_units_both_ways).
% 1.67/1.89 dependent: set(dynamic_demod_all).
% 1.67/1.89 dependent: set(dynamic_demod).
% 1.67/1.89 dependent: set(order_eq).
% 1.67/1.89 dependent: set(back_demod).
% 1.67/1.89 dependent: set(lrpo).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=11): 1 [] mult(mult(x0,x1),op_c)!=mult(x0,mult(x1,op_c)).
% 1.67/1.89
% 1.67/1.89 ------------> process sos:
% 1.67/1.89 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.67/1.89 ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.67/1.89 ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.67/1.89 ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.67/1.89 ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.67/1.89 ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.67/1.89 ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.67/1.89 ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.67/1.89 ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.67/1.89 ** KEPT (pick-wt=5): 11 [] mult(A,unit)=A.
% 1.67/1.89 ---> New Demodulator: 12 [new_demod,11] mult(A,unit)=A.
% 1.67/1.89 ** KEPT (pick-wt=5): 13 [] mult(unit,A)=A.
% 1.67/1.89 ---> New Demodulator: 14 [new_demod,13] mult(unit,A)=A.
% 1.67/1.89 ** KEPT (pick-wt=15): 16 [copy,15,flip.1] mult(rd(mult(A,B),A),mult(A,C))=mult(A,mult(B,C)).
% 1.67/1.89 ---> New Demodulator: 17 [new_demod,16] mult(rd(mult(A,B),A),mult(A,C))=mult(A,mult(B,C)).
% 1.67/1.89 ** KEPT (pick-wt=15): 18 [] mult(mult(A,B),C)=mult(mult(A,C),ld(C,mult(B,C))).
% 1.67/1.89 ** KEPT (pick-wt=7): 19 [] mult(op_c,A)=mult(A,op_c).
% 1.67/1.89 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.67/1.89 >>>> Starting back demodulation with 4.
% 1.67/1.89 >>>> Starting back demodulation with 6.
% 1.67/1.89 >>>> Starting back demodulation with 8.
% 1.67/1.89 >>>> Starting back demodulation with 10.
% 1.67/1.89 >>>> Starting back demodulation with 12.
% 1.67/1.89 >>>> Starting back demodulation with 14.
% 1.67/1.89 >>>> Starting back demodulation with 17.
% 1.67/1.89 ** KEPT (pick-wt=15): 20 [copy,18,flip.1] mult(mult(A,B),ld(B,mult(C,B)))=mult(mult(A,C),B).
% 1.67/1.89 ** KEPT (pick-wt=7): 21 [copy,19,flip.1] mult(A,op_c)=mult(op_c,A).
% 1.67/1.89 Following clause subsumed by 18 during input processing: 0 [copy,20,flip.1] mult(mult(A,B),C)=mult(mult(A,C),ld(C,mult(B,C))).
% 1.67/1.89 Following clause subsumed by 19 during input processing: 0 [copy,21,flip.1] mult(op_c,A)=mult(A,op_c).
% 1.67/1.89
% 1.67/1.89 ======= end of input processing =======
% 1.67/1.89
% 1.67/1.89 =========== start of search ===========
% 1.67/1.89
% 1.67/1.89 -------- PROOF --------
% 1.67/1.89
% 1.67/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 137 [binary,136.1,112.1] $F.
% 1.67/1.89
% 1.67/1.89 Length of proof is 8. Level of proof is 4.
% 1.67/1.89
% 1.67/1.89 ---------------- PROOF ----------------
% 1.67/1.89 % SZS status Unsatisfiable
% 1.67/1.89 % SZS output start Refutation
% See solution above
% 1.67/1.89 ------------ end of proof -------------
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89 ============ end of search ============
% 1.67/1.89
% 1.67/1.89 -------------- statistics -------------
% 1.67/1.89 clauses given 26
% 1.67/1.89 clauses generated 231
% 1.67/1.89 clauses kept 81
% 1.67/1.89 clauses forward subsumed 195
% 1.67/1.89 clauses back subsumed 0
% 1.67/1.89 Kbytes malloced 1953
% 1.67/1.89
% 1.67/1.89 ----------- times (seconds) -----------
% 1.67/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.67/1.89
% 1.67/1.89 That finishes the proof of the theorem.
% 1.67/1.89
% 1.67/1.89 Process 6019 finished Wed Jul 27 05:13:07 2022
% 1.67/1.89 Otter interrupted
% 1.67/1.89 PROOF FOUND
%------------------------------------------------------------------------------