TSTP Solution File: GRP194+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 12:56:43 EDT 2022
% Result : Theorem 1.74s 1.95s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 11 unt; 1 nHn; 20 RR)
% Number of literals : 34 ( 8 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ group_member(A,f)
| group_member(phi(A),h) ),
file('GRP194+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ group_member(A,f)
| ~ group_member(B,f)
| multiply(h,phi(A),phi(B)) = phi(multiply(f,A,B)) ),
file('GRP194+1.p',unknown),
[] ).
cnf(5,plain,
( ~ group_member(A,f)
| ~ group_member(B,f)
| phi(multiply(f,A,B)) = multiply(h,phi(A),phi(B)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.3')] ).
cnf(6,axiom,
( ~ group_member(A,h)
| group_member(dollar_f1(A),f) ),
file('GRP194+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ group_member(A,h)
| phi(dollar_f1(A)) = A ),
file('GRP194+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ left_zero(A,B)
| group_member(B,A) ),
file('GRP194+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ left_zero(A,B)
| ~ group_member(C,A)
| multiply(A,B,C) = B ),
file('GRP194+1.p',unknown),
[] ).
cnf(10,axiom,
( left_zero(A,B)
| ~ group_member(B,A)
| group_member(dollar_f2(A,B),A) ),
file('GRP194+1.p',unknown),
[] ).
cnf(11,axiom,
( left_zero(A,B)
| ~ group_member(B,A)
| multiply(A,B,dollar_f2(A,B)) != B ),
file('GRP194+1.p',unknown),
[] ).
cnf(12,axiom,
~ left_zero(h,phi(f_left_zero)),
file('GRP194+1.p',unknown),
[] ).
cnf(20,axiom,
left_zero(f,f_left_zero),
file('GRP194+1.p',unknown),
[] ).
cnf(21,plain,
group_member(f_left_zero,f),
inference(hyper,[status(thm)],[20,8]),
[iquote('hyper,20,8')] ).
cnf(31,plain,
group_member(phi(f_left_zero),h),
inference(hyper,[status(thm)],[21,3]),
[iquote('hyper,21,3')] ).
cnf(32,plain,
group_member(dollar_f2(h,phi(f_left_zero)),h),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[31,10]),12]),
[iquote('hyper,31,10,unit_del,12')] ).
cnf(83,plain,
phi(dollar_f1(dollar_f2(h,phi(f_left_zero)))) = dollar_f2(h,phi(f_left_zero)),
inference(hyper,[status(thm)],[32,7]),
[iquote('hyper,32,7')] ).
cnf(84,plain,
group_member(dollar_f1(dollar_f2(h,phi(f_left_zero))),f),
inference(hyper,[status(thm)],[32,6]),
[iquote('hyper,32,6')] ).
cnf(118,plain,
multiply(f,f_left_zero,dollar_f1(dollar_f2(h,phi(f_left_zero)))) = f_left_zero,
inference(hyper,[status(thm)],[84,9,20]),
[iquote('hyper,84,9,20')] ).
cnf(121,plain,
multiply(h,phi(f_left_zero),dollar_f2(h,phi(f_left_zero))) = phi(f_left_zero),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[84,5,21]),118,83])]),
[iquote('hyper,84,5,21,demod,118,83,flip.1')] ).
cnf(517,plain,
left_zero(h,phi(f_left_zero)),
inference(hyper,[status(thm)],[121,11,31]),
[iquote('hyper,121,11,31')] ).
cnf(518,plain,
$false,
inference(binary,[status(thm)],[517,12]),
[iquote('binary,517.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 05:27:37 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.74/1.95 ----- Otter 3.3f, August 2004 -----
% 1.74/1.95 The process was started by sandbox on n016.cluster.edu,
% 1.74/1.95 Wed Jul 27 05:27:37 2022
% 1.74/1.95 The command was "./otter". The process ID is 7592.
% 1.74/1.95
% 1.74/1.95 set(prolog_style_variables).
% 1.74/1.95 set(auto).
% 1.74/1.95 dependent: set(auto1).
% 1.74/1.95 dependent: set(process_input).
% 1.74/1.95 dependent: clear(print_kept).
% 1.74/1.95 dependent: clear(print_new_demod).
% 1.74/1.95 dependent: clear(print_back_demod).
% 1.74/1.95 dependent: clear(print_back_sub).
% 1.74/1.95 dependent: set(control_memory).
% 1.74/1.95 dependent: assign(max_mem, 12000).
% 1.74/1.95 dependent: assign(pick_given_ratio, 4).
% 1.74/1.95 dependent: assign(stats_level, 1).
% 1.74/1.95 dependent: assign(max_seconds, 10800).
% 1.74/1.95 clear(print_given).
% 1.74/1.95
% 1.74/1.95 formula_list(usable).
% 1.74/1.95 all A (A=A).
% 1.74/1.95 all G X Y (group_member(X,G)&group_member(Y,G)->group_member(multiply(G,X,Y),G)).
% 1.74/1.95 all G X Y Z (group_member(X,G)&group_member(Y,G)&group_member(Z,G)->multiply(G,multiply(G,X,Y),Z)=multiply(G,X,multiply(G,Y,Z))).
% 1.74/1.95 all X (group_member(X,f)->group_member(phi(X),h)).
% 1.74/1.95 all X Y (group_member(X,f)&group_member(Y,f)->multiply(h,phi(X),phi(Y))=phi(multiply(f,X,Y))).
% 1.74/1.95 all X (group_member(X,h)-> (exists Y (group_member(Y,f)&phi(Y)=X))).
% 1.74/1.95 all G X (left_zero(G,X)<->group_member(X,G)& (all Y (group_member(Y,G)->multiply(G,X,Y)=X))).
% 1.74/1.95 left_zero(f,f_left_zero).
% 1.74/1.95 -left_zero(h,phi(f_left_zero)).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 -------> usable clausifies to:
% 1.74/1.95
% 1.74/1.95 list(usable).
% 1.74/1.95 0 [] A=A.
% 1.74/1.95 0 [] -group_member(X,G)| -group_member(Y,G)|group_member(multiply(G,X,Y),G).
% 1.74/1.95 0 [] -group_member(X,G)| -group_member(Y,G)| -group_member(Z,G)|multiply(G,multiply(G,X,Y),Z)=multiply(G,X,multiply(G,Y,Z)).
% 1.74/1.95 0 [] -group_member(X,f)|group_member(phi(X),h).
% 1.74/1.95 0 [] -group_member(X,f)| -group_member(Y,f)|multiply(h,phi(X),phi(Y))=phi(multiply(f,X,Y)).
% 1.74/1.95 0 [] -group_member(X,h)|group_member($f1(X),f).
% 1.74/1.95 0 [] -group_member(X,h)|phi($f1(X))=X.
% 1.74/1.95 0 [] -left_zero(G,X)|group_member(X,G).
% 1.74/1.95 0 [] -left_zero(G,X)| -group_member(Y,G)|multiply(G,X,Y)=X.
% 1.74/1.95 0 [] left_zero(G,X)| -group_member(X,G)|group_member($f2(G,X),G).
% 1.74/1.95 0 [] left_zero(G,X)| -group_member(X,G)|multiply(G,X,$f2(G,X))!=X.
% 1.74/1.95 0 [] left_zero(f,f_left_zero).
% 1.74/1.95 0 [] -left_zero(h,phi(f_left_zero)).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.74/1.95
% 1.74/1.95 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.95 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.95 deletion, with positive clauses in sos and nonpositive
% 1.74/1.95 clauses in usable.
% 1.74/1.95
% 1.74/1.95 dependent: set(knuth_bendix).
% 1.74/1.95 dependent: set(anl_eq).
% 1.74/1.95 dependent: set(para_from).
% 1.74/1.95 dependent: set(para_into).
% 1.74/1.95 dependent: clear(para_from_right).
% 1.74/1.95 dependent: clear(para_into_right).
% 1.74/1.95 dependent: set(para_from_vars).
% 1.74/1.95 dependent: set(eq_units_both_ways).
% 1.74/1.95 dependent: set(dynamic_demod_all).
% 1.74/1.95 dependent: set(dynamic_demod).
% 1.74/1.95 dependent: set(order_eq).
% 1.74/1.95 dependent: set(back_demod).
% 1.74/1.95 dependent: set(lrpo).
% 1.74/1.95 dependent: set(hyper_res).
% 1.74/1.95 dependent: set(unit_deletion).
% 1.74/1.95 dependent: set(factor).
% 1.74/1.95
% 1.74/1.95 ------------> process usable:
% 1.74/1.95 ** KEPT (pick-wt=12): 1 [] -group_member(A,B)| -group_member(C,B)|group_member(multiply(B,A,C),B).
% 1.74/1.95 ** KEPT (pick-wt=24): 2 [] -group_member(A,B)| -group_member(C,B)| -group_member(D,B)|multiply(B,multiply(B,A,C),D)=multiply(B,A,multiply(B,C,D)).
% 1.74/1.95 ** KEPT (pick-wt=7): 3 [] -group_member(A,f)|group_member(phi(A),h).
% 1.74/1.95 ** KEPT (pick-wt=18): 5 [copy,4,flip.3] -group_member(A,f)| -group_member(B,f)|phi(multiply(f,A,B))=multiply(h,phi(A),phi(B)).
% 1.74/1.95 ** KEPT (pick-wt=7): 6 [] -group_member(A,h)|group_member($f1(A),f).
% 1.74/1.95 ** KEPT (pick-wt=8): 7 [] -group_member(A,h)|phi($f1(A))=A.
% 1.74/1.95 ** KEPT (pick-wt=6): 8 [] -left_zero(A,B)|group_member(B,A).
% 1.74/1.95 ** KEPT (pick-wt=12): 9 [] -left_zero(A,B)| -group_member(C,A)|multiply(A,B,C)=B.
% 1.74/1.95 ** KEPT (pick-wt=11): 10 [] left_zero(A,B)| -group_member(B,A)|group_member($f2(A,B),A).
% 1.74/1.95 ** KEPT (pick-wt=14): 11 [] left_zero(A,B)| -group_member(B,A)|multiply(A,B,$f2(A,B))!=B.
% 1.74/1.95 ** KEPT (pick-wt=4): 12 [] -left_zero(h,phi(f_left_zero)).
% 1.74/1.95
% 1.74/1.95 ------------> process sos:
% 1.74/1.95 ** KEPT (pick-wt=3): 19 [] A=A.
% 1.74/1.95 ** KEPT (pick-wt=3): 20 [] left_zero(f,f_left_zero).
% 1.74/1.95 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] A=A.
% 1.74/1.95
% 1.74/1.95 ======= end of input processing =======
% 1.74/1.95
% 1.74/1.95 =========== start of search ===========
% 1.74/1.95
% 1.74/1.95 -------- PROOF --------
% 1.74/1.95
% 1.74/1.95 ----> UNIT CONFLICT at 0.02 sec ----> 518 [binary,517.1,12.1] $F.
% 1.74/1.95
% 1.74/1.95 Length of proof is 9. Level of proof is 7.
% 1.74/1.95
% 1.74/1.95 ---------------- PROOF ----------------
% 1.74/1.95 % SZS status Theorem
% 1.74/1.95 % SZS output start Refutation
% See solution above
% 1.74/1.95 ------------ end of proof -------------
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95 ============ end of search ============
% 1.74/1.95
% 1.74/1.95 -------------- statistics -------------
% 1.74/1.95 clauses given 22
% 1.74/1.95 clauses generated 734
% 1.74/1.95 clauses kept 289
% 1.74/1.95 clauses forward subsumed 508
% 1.74/1.95 clauses back subsumed 0
% 1.74/1.95 Kbytes malloced 2929
% 1.74/1.95
% 1.74/1.95 ----------- times (seconds) -----------
% 1.74/1.95 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.74/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.95 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.95
% 1.74/1.95 That finishes the proof of the theorem.
% 1.74/1.95
% 1.74/1.95 Process 7592 finished Wed Jul 27 05:27:38 2022
% 1.74/1.95 Otter interrupted
% 1.74/1.95 PROOF FOUND
%------------------------------------------------------------------------------