%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 12:57:45 EDT 2022
% Result : Theorem 2.03s 2.24s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 10 unt; 2 nHn; 8 RR)
% Number of literals : 14 ( 13 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(mult(a,b),c) != mult(a,mult(b,c)),
file('GRP747+1.p',unknown),
[] ).
cnf(14,axiom,
mult(unit,A) = A,
file('GRP747+1.p',unknown),
[] ).
cnf(17,axiom,
( mult(mult(A,B),C) = mult(A,mult(C,B))
| mult(mult(A,B),C) = mult(mult(A,C),B) ),
file('GRP747+1.p',unknown),
[] ).
cnf(19,axiom,
( mult(mult(A,B),C) = mult(A,mult(C,B))
| mult(mult(A,C),B) = mult(mult(A,B),C) ),
file('GRP747+1.p',unknown),
[] ).
cnf(71,plain,
mult(A,B) = mult(B,A),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,14]),14,14,14])]),
[iquote('para_into,17.1.1.1,13.1.1,demod,14,14,14,factor_simp')] ).
cnf(115,plain,
mult(mult(b,a),c) != mult(a,mult(b,c)),
inference(para_from,[status(thm),theory(equality)],[71,1]),
[iquote('para_from,71.1.1,1.1.1.1')] ).
cnf(356,plain,
mult(mult(b,c),a) = mult(b,mult(a,c)),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[115,19]),71]),
[iquote('para_into,115.1.1,19.2.1,unit_del,71')] ).
cnf(992,plain,
mult(b,mult(a,c)) = mult(a,mult(b,c)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[356,71])]),
[iquote('para_into,356.1.1,71.1.1,flip.1')] ).
cnf(994,plain,
mult(mult(b,a),c) = mult(b,mult(c,a)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[356,19]),992]),115]),
[iquote('para_into,356.1.1,19.2.1,demod,992,unit_del,115')] ).
cnf(997,plain,
mult(b,mult(c,a)) != mult(a,mult(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[115]),994]),
[iquote('back_demod,115,demod,994')] ).
cnf(1995,plain,
mult(b,mult(c,a)) = mult(a,mult(b,c)),
inference(para_into,[status(thm),theory(equality)],[992,71]),
[iquote('para_into,991.1.1.2,71.1.1')] ).
cnf(1997,plain,
$false,
inference(binary,[status(thm)],[1995,997]),
[iquote('binary,1995.1,997.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 05:23:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.92/2.10 ----- Otter 3.3f, August 2004 -----
% 1.92/2.10 The process was started by sandbox on n011.cluster.edu,
% 1.92/2.10 Wed Jul 27 05:23:40 2022
% 1.92/2.10 The command was "./otter". The process ID is 27246.
% 1.92/2.10
% 1.92/2.10 set(prolog_style_variables).
% 1.92/2.10 set(auto).
% 1.92/2.10 dependent: set(auto1).
% 1.92/2.10 dependent: set(process_input).
% 1.92/2.10 dependent: clear(print_kept).
% 1.92/2.10 dependent: clear(print_new_demod).
% 1.92/2.10 dependent: clear(print_back_demod).
% 1.92/2.10 dependent: clear(print_back_sub).
% 1.92/2.10 dependent: set(control_memory).
% 1.92/2.10 dependent: assign(max_mem, 12000).
% 1.92/2.10 dependent: assign(pick_given_ratio, 4).
% 1.92/2.10 dependent: assign(stats_level, 1).
% 1.92/2.10 dependent: assign(max_seconds, 10800).
% 1.92/2.10 clear(print_given).
% 1.92/2.10
% 1.92/2.10 formula_list(usable).
% 1.92/2.10 all A (A=A).
% 1.92/2.10 all B A (mult(A,ld(A,B))=B).
% 1.92/2.10 all B A (ld(A,mult(A,B))=B).
% 1.92/2.10 all B A (mult(rd(A,B),B)=A).
% 1.92/2.10 all B A (rd(mult(A,B),B)=A).
% 1.92/2.10 all A (mult(A,unit)=A).
% 1.92/2.10 all A (mult(unit,A)=A).
% 1.92/2.10 all C B A (mult(mult(mult(A,B),C),B)=mult(A,mult(mult(B,C),B))).
% 1.92/2.10 all X0 X1 X2 (mult(mult(X0,X1),X2)=mult(X0,mult(X2,X1))&mult(mult(X0,X2),X1)=mult(X0,mult(X1,X2))|mult(mult(X0,X1),X2)=mult(mult(X0,X2),X1)&mult(X0,mult(X1,X2))=mult(X0,mult(X2,X1))).
% 1.92/2.10 mult(mult(a,b),c)!=mult(a,mult(b,c)).
% 1.92/2.10 end_of_list.
% 1.92/2.10
% 1.92/2.10 -------> usable clausifies to:
% 1.92/2.10
% 1.92/2.10 list(usable).
% 1.92/2.10 0 [] A=A.
% 1.92/2.10 0 [] mult(A,ld(A,B))=B.
% 1.92/2.10 0 [] ld(A,mult(A,B))=B.
% 1.92/2.10 0 [] mult(rd(A,B),B)=A.
% 1.92/2.10 0 [] rd(mult(A,B),B)=A.
% 1.92/2.10 0 [] mult(A,unit)=A.
% 1.92/2.10 0 [] mult(unit,A)=A.
% 1.92/2.10 0 [] mult(mult(mult(A,B),C),B)=mult(A,mult(mult(B,C),B)).
% 1.92/2.10 0 [] mult(mult(X0,X1),X2)=mult(X0,mult(X2,X1))|mult(mult(X0,X1),X2)=mult(mult(X0,X2),X1).
% 1.92/2.10 0 [] mult(mult(X0,X1),X2)=mult(X0,mult(X2,X1))|mult(X0,mult(X1,X2))=mult(X0,mult(X2,X1)).
% 1.92/2.10 0 [] mult(mult(X0,X2),X1)=mult(X0,mult(X1,X2))|mult(mult(X0,X1),X2)=mult(mult(X0,X2),X1).
% 1.92/2.10 0 [] mult(mult(X0,X2),X1)=mult(X0,mult(X1,X2))|mult(X0,mult(X1,X2))=mult(X0,mult(X2,X1)).
% 1.92/2.10 0 [] mult(mult(a,b),c)!=mult(a,mult(b,c)).
% 1.92/2.10 end_of_list.
% 1.92/2.10
% 1.92/2.10 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.92/2.10
% 1.92/2.10 This ia a non-Horn set with equality. The strategy will be
% 1.92/2.10 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.92/2.10 deletion, with positive clauses in sos and nonpositive
% 1.92/2.10 clauses in usable.
% 1.92/2.10
% 1.92/2.10 dependent: set(knuth_bendix).
% 1.92/2.10 dependent: set(anl_eq).
% 1.92/2.10 dependent: set(para_from).
% 1.92/2.10 dependent: set(para_into).
% 1.92/2.10 dependent: clear(para_from_right).
% 1.92/2.10 dependent: clear(para_into_right).
% 1.92/2.10 dependent: set(para_from_vars).
% 1.92/2.10 dependent: set(eq_units_both_ways).
% 1.92/2.10 dependent: set(dynamic_demod_all).
% 1.92/2.10 dependent: set(dynamic_demod).
% 1.92/2.10 dependent: set(order_eq).
% 1.92/2.10 dependent: set(back_demod).
% 1.92/2.10 dependent: set(lrpo).
% 1.92/2.10 dependent: set(hyper_res).
% 1.92/2.10 dependent: set(unit_deletion).
% 1.92/2.10 dependent: set(factor).
% 1.92/2.10
% 1.92/2.10 ------------> process usable:
% 1.92/2.10 ** KEPT (pick-wt=11): 1 [] mult(mult(a,b),c)!=mult(a,mult(b,c)).
% 1.92/2.10
% 1.92/2.10 ------------> process sos:
% 1.92/2.10 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.92/2.10 ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.92/2.10 ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.92/2.10 ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.92/2.10 ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.92/2.10 ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.92/2.10 ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.92/2.10 ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.92/2.10 ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.92/2.10 ** KEPT (pick-wt=5): 11 [] mult(A,unit)=A.
% 1.92/2.10 ---> New Demodulator: 12 [new_demod,11] mult(A,unit)=A.
% 1.92/2.10 ** KEPT (pick-wt=5): 13 [] mult(unit,A)=A.
% 1.92/2.10 ---> New Demodulator: 14 [new_demod,13] mult(unit,A)=A.
% 1.92/2.10 ** KEPT (pick-wt=15): 15 [] mult(mult(mult(A,B),C),B)=mult(A,mult(mult(B,C),B)).
% 1.92/2.10 ---> New Demodulator: 16 [new_demod,15] mult(mult(mult(A,B),C),B)=mult(A,mult(mult(B,C),B)).
% 1.92/2.10 ** KEPT (pick-wt=22): 17 [] mult(mult(A,B),C)=mult(A,mult(C,B))|mult(mult(A,B),C)=mult(mult(A,C),B).
% 1.92/2.10 ** KEPT (pick-wt=22): 18 [] mult(mult(A,B),C)=mult(A,mult(C,B))|mult(A,mult(B,C))=mult(A,mult(C,B)).
% 1.92/2.10 ** KEPT (pick-wt=22): 19 [] mult(mult(A,B),C)=mult(A,mult(C,B))|mult(mult(A,C),B)=mult(mult(A,B),C).
% 1.92/2.10 ** KEPT (pick-wt=22): 20 [] mult(mult(A,B),C)=mult(A,mult(C,B))|mult(A,mult(C,B))=mult(A,mult(B,C)).
% 1.92/2.10 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.92/2.10 >>>> Starting back demodulation with 4.
% 1.92/2.10 >>>> Starting back demodulation with 6.
% 1.92/2.10 >>>> Starting back demodulation with 8.
% 2.03/2.24 >>>> Starting back demodulation with 10.
% 2.03/2.24 >>>> Starting back demodulation with 12.
% 2.03/2.24 >>>> Starting back demodulation with 14.
% 2.03/2.24 >>>> Starting back demodulation with 16.
% 2.03/2.24
% 2.03/2.24 ======= end of input processing =======
% 2.03/2.24
% 2.03/2.24 =========== start of search ===========
% 2.03/2.24
% 2.03/2.24
% 2.03/2.24 Resetting weight limit to 17.
% 2.03/2.24
% 2.03/2.24
% 2.03/2.24 Resetting weight limit to 17.
% 2.03/2.24
% 2.03/2.24 sos_size=790
% 2.03/2.24
% 2.03/2.24 -------- PROOF --------
% 2.03/2.24
% 2.03/2.24 ----> UNIT CONFLICT at 0.14 sec ----> 1997 [binary,1995.1,997.1] $F.
% 2.03/2.24
% 2.03/2.24 Length of proof is 7. Level of proof is 6.
% 2.03/2.24
% 2.03/2.24 ---------------- PROOF ----------------
% 2.03/2.24 % SZS status Theorem
% 2.03/2.24 % SZS output start Refutation
% See solution above
% 2.03/2.24 ------------ end of proof -------------
% 2.03/2.24
% 2.03/2.24
% 2.03/2.24 Search stopped by max_proofs option.
% 2.03/2.24
% 2.03/2.24
% 2.03/2.24 Search stopped by max_proofs option.
% 2.03/2.24
% 2.03/2.24 ============ end of search ============
% 2.03/2.24
% 2.03/2.24 -------------- statistics -------------
% 2.03/2.24 clauses given 57
% 2.03/2.24 clauses generated 2670
% 2.03/2.24 clauses kept 1711
% 2.03/2.24 clauses forward subsumed 1369
% 2.03/2.24 clauses back subsumed 3
% 2.03/2.24 Kbytes malloced 4882
% 2.03/2.24
% 2.03/2.24 ----------- times (seconds) -----------
% 2.03/2.24 user CPU time 0.14 (0 hr, 0 min, 0 sec)
% 2.03/2.24 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.03/2.24 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.03/2.24
% 2.03/2.24 That finishes the proof of the theorem.
% 2.03/2.24
% 2.03/2.24 Process 27246 finished Wed Jul 27 05:23:42 2022
% 2.03/2.24 Otter interrupted
% 2.03/2.24 PROOF FOUND
%------------------------------------------------------------------------------