%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP656+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 12:57:34 EDT 2022
% Result : Theorem 1.99s 2.14s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 16 ( 15 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( mult(dollar_f1(A),A) != dollar_f1(A)
| mult(A,dollar_f1(A)) != dollar_f1(A) ),
file('GRP656+1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP656+1.p',unknown),
[] ).
cnf(3,axiom,
mult(A,ld(A,B)) = B,
file('GRP656+1.p',unknown),
[] ).
cnf(5,axiom,
ld(A,mult(A,B)) = B,
file('GRP656+1.p',unknown),
[] ).
cnf(9,axiom,
rd(mult(A,B),B) = A,
file('GRP656+1.p',unknown),
[] ).
cnf(11,axiom,
mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
file('GRP656+1.p',unknown),
[] ).
cnf(12,plain,
mult(mult(A,mult(B,C)),A) = mult(mult(A,B),mult(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(21,plain,
mult(mult(A,B),A) = mult(mult(A,C),mult(ld(C,B),A)),
inference(para_into,[status(thm),theory(equality)],[12,3]),
[iquote('para_into,12.1.1.1.2,3.1.1')] ).
cnf(70,plain,
ld(mult(A,B),mult(mult(A,C),mult(ld(C,B),A))) = A,
inference(para_from,[status(thm),theory(equality)],[21,5]),
[iquote('para_from,21.1.1,5.1.1.2')] ).
cnf(353,plain,
mult(ld(A,A),B) = B,
inference(para_into,[status(thm),theory(equality)],[70,5]),
[iquote('para_into,70.1.1,5.1.1')] ).
cnf(379,plain,
rd(A,A) = ld(B,B),
inference(para_from,[status(thm),theory(equality)],[353,9]),
[iquote('para_from,353.1.1,9.1.1.1')] ).
cnf(382,plain,
ld(A,A) = rd(B,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[379])]),
[iquote('copy,379,flip.1')] ).
cnf(391,plain,
mult(rd(A,A),B) = B,
inference(para_from,[status(thm),theory(equality)],[382,353]),
[iquote('para_from,382.1.1,353.1.1.1')] ).
cnf(396,plain,
mult(A,rd(B,B)) = A,
inference(para_from,[status(thm),theory(equality)],[382,3]),
[iquote('para_from,382.1.1,3.1.1.2')] ).
cnf(433,plain,
dollar_f1(rd(A,A)) != dollar_f1(rd(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[391,1]),396]),
[iquote('para_from,391.1.1,1.2.1,demod,396')] ).
cnf(434,plain,
$false,
inference(binary,[status(thm)],[433,2]),
[iquote('binary,433.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP656+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 05:41:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.14 ----- Otter 3.3f, August 2004 -----
% 1.96/2.14 The process was started by sandbox on n026.cluster.edu,
% 1.96/2.14 Wed Jul 27 05:41:39 2022
% 1.96/2.14 The command was "./otter". The process ID is 27115.
% 1.96/2.14
% 1.96/2.14 set(prolog_style_variables).
% 1.96/2.14 set(auto).
% 1.96/2.14 dependent: set(auto1).
% 1.96/2.14 dependent: set(process_input).
% 1.96/2.14 dependent: clear(print_kept).
% 1.96/2.14 dependent: clear(print_new_demod).
% 1.96/2.14 dependent: clear(print_back_demod).
% 1.96/2.14 dependent: clear(print_back_sub).
% 1.96/2.14 dependent: set(control_memory).
% 1.96/2.14 dependent: assign(max_mem, 12000).
% 1.96/2.14 dependent: assign(pick_given_ratio, 4).
% 1.96/2.14 dependent: assign(stats_level, 1).
% 1.96/2.14 dependent: assign(max_seconds, 10800).
% 1.96/2.14 clear(print_given).
% 1.96/2.14
% 1.96/2.14 formula_list(usable).
% 1.96/2.14 all A (A=A).
% 1.96/2.14 all B A (mult(A,ld(A,B))=B).
% 1.96/2.14 all B A (ld(A,mult(A,B))=B).
% 1.96/2.14 all B A (mult(rd(A,B),B)=A).
% 1.96/2.14 all B A (rd(mult(A,B),B)=A).
% 1.96/2.14 all C B A (mult(mult(A,B),mult(C,A))=mult(mult(A,mult(B,C)),A)).
% 1.96/2.14 -(exists X0 all X1 (mult(X1,X0)=X1&mult(X0,X1)=X1)).
% 1.96/2.14 end_of_list.
% 1.96/2.14
% 1.96/2.14 -------> usable clausifies to:
% 1.96/2.14
% 1.96/2.14 list(usable).
% 1.96/2.14 0 [] A=A.
% 1.96/2.14 0 [] mult(A,ld(A,B))=B.
% 1.96/2.14 0 [] ld(A,mult(A,B))=B.
% 1.96/2.14 0 [] mult(rd(A,B),B)=A.
% 1.96/2.14 0 [] rd(mult(A,B),B)=A.
% 1.96/2.14 0 [] mult(mult(A,B),mult(C,A))=mult(mult(A,mult(B,C)),A).
% 1.96/2.14 0 [] mult($f1(X0),X0)!=$f1(X0)|mult(X0,$f1(X0))!=$f1(X0).
% 1.96/2.14 end_of_list.
% 1.96/2.14
% 1.96/2.14 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.96/2.14
% 1.96/2.14 This is a Horn set with equality. The strategy will be
% 1.96/2.14 Knuth-Bendix and hyper_res, with positive clauses in
% 1.96/2.14 sos and nonpositive clauses in usable.
% 1.96/2.14
% 1.96/2.14 dependent: set(knuth_bendix).
% 1.96/2.14 dependent: set(anl_eq).
% 1.96/2.14 dependent: set(para_from).
% 1.96/2.14 dependent: set(para_into).
% 1.96/2.14 dependent: clear(para_from_right).
% 1.96/2.14 dependent: clear(para_into_right).
% 1.96/2.14 dependent: set(para_from_vars).
% 1.96/2.14 dependent: set(eq_units_both_ways).
% 1.96/2.14 dependent: set(dynamic_demod_all).
% 1.96/2.14 dependent: set(dynamic_demod).
% 1.96/2.14 dependent: set(order_eq).
% 1.96/2.14 dependent: set(back_demod).
% 1.96/2.14 dependent: set(lrpo).
% 1.96/2.14 dependent: set(hyper_res).
% 1.96/2.14 dependent: clear(order_hyper).
% 1.96/2.14
% 1.96/2.14 ------------> process usable:
% 1.96/2.14 ** KEPT (pick-wt=14): 1 [] mult($f1(A),A)!=$f1(A)|mult(A,$f1(A))!=$f1(A).
% 1.96/2.14
% 1.96/2.14 ------------> process sos:
% 1.96/2.14 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.96/2.14 ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.96/2.14 ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.96/2.14 ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.96/2.14 ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.96/2.14 ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.96/2.14 ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.96/2.14 ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.96/2.14 ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.96/2.14 ** KEPT (pick-wt=15): 12 [copy,11,flip.1] mult(mult(A,mult(B,C)),A)=mult(mult(A,B),mult(C,A)).
% 1.96/2.14 ---> New Demodulator: 13 [new_demod,12] mult(mult(A,mult(B,C)),A)=mult(mult(A,B),mult(C,A)).
% 1.96/2.14 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.96/2.14 >>>> Starting back demodulation with 4.
% 1.96/2.14 >>>> Starting back demodulation with 6.
% 1.96/2.14 >>>> Starting back demodulation with 8.
% 1.96/2.14 >>>> Starting back demodulation with 10.
% 1.96/2.14 >>>> Starting back demodulation with 13.
% 1.96/2.14
% 1.96/2.14 ======= end of input processing =======
% 1.96/2.14
% 1.96/2.14 =========== start of search ===========
% 1.96/2.14
% 1.96/2.14
% 1.96/2.14 Resetting weight limit to 15.
% 1.96/2.14
% 1.96/2.14
% 1.96/2.14 Resetting weight limit to 15.
% 1.99/2.14
% 1.99/2.14 sos_size=184
% 1.99/2.14
% 1.99/2.14 -------- PROOF --------
% 1.99/2.14
% 1.99/2.14 ----> UNIT CONFLICT at 0.04 sec ----> 434 [binary,433.1,2.1] $F.
% 1.99/2.14
% 1.99/2.14 Length of proof is 9. Level of proof is 8.
% 1.99/2.14
% 1.99/2.14 ---------------- PROOF ----------------
% 1.99/2.14 % SZS status Theorem
% 1.99/2.14 % SZS output start Refutation
% See solution above
% 1.99/2.14 ------------ end of proof -------------
% 1.99/2.14
% 1.99/2.14
% 1.99/2.14 Search stopped by max_proofs option.
% 1.99/2.14
% 1.99/2.14
% 1.99/2.14 Search stopped by max_proofs option.
% 1.99/2.14
% 1.99/2.14 ============ end of search ============
% 1.99/2.14
% 1.99/2.14 -------------- statistics -------------
% 1.99/2.14 clauses given 32
% 1.99/2.14 clauses generated 812
% 1.99/2.14 clauses kept 281
% 1.99/2.14 clauses forward subsumed 381
% 1.99/2.14 clauses back subsumed 0
% 1.99/2.14 Kbytes malloced 4882
% 1.99/2.14
% 1.99/2.14 ----------- times (seconds) -----------
% 1.99/2.14 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.99/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.14 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.99/2.14
% 1.99/2.14 That finishes the proof of the theorem.
% 1.99/2.14
% 1.99/2.14 Process 27115 finished Wed Jul 27 05:41:40 2022
% 1.99/2.15 Otter interrupted
% 1.99/2.15 PROOF FOUND
%------------------------------------------------------------------------------