%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP658+1 : TPTP v8.1.0. Released v4.0.0.
% 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 12:57:34 EDT 2022
% Result : Theorem 1.92s 2.11s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of clauses : 38 ( 37 unt; 0 nHn; 3 RR)
% Number of literals : 39 ( 38 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 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 : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( mult(dollar_f1(A),A) != dollar_f1(A)
| mult(A,dollar_f1(A)) != dollar_f1(A) ),
file('GRP658+1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP658+1.p',unknown),
[] ).
cnf(4,axiom,
mult(A,ld(A,B)) = B,
file('GRP658+1.p',unknown),
[] ).
cnf(5,axiom,
ld(A,mult(A,B)) = B,
file('GRP658+1.p',unknown),
[] ).
cnf(8,axiom,
mult(rd(A,B),B) = A,
file('GRP658+1.p',unknown),
[] ).
cnf(10,axiom,
rd(mult(A,B),B) = A,
file('GRP658+1.p',unknown),
[] ).
cnf(11,axiom,
mult(mult(A,mult(B,B)),C) = mult(mult(A,B),mult(B,C)),
file('GRP658+1.p',unknown),
[] ).
cnf(15,plain,
rd(A,ld(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[10,4]),
[iquote('para_into,9.1.1.1,3.1.1')] ).
cnf(21,plain,
mult(mult(rd(A,mult(B,B)),B),mult(B,C)) = mult(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,8])]),
[iquote('para_into,11.1.1.1,7.1.1,flip.1')] ).
cnf(23,plain,
mult(mult(A,B),mult(B,ld(mult(A,mult(B,B)),C))) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,4])]),
[iquote('para_into,11.1.1,3.1.1,flip.1')] ).
cnf(25,plain,
rd(mult(mult(A,B),mult(B,C)),C) = mult(A,mult(B,B)),
inference(para_from,[status(thm),theory(equality)],[11,10]),
[iquote('para_from,11.1.1,9.1.1.1')] ).
cnf(36,plain,
mult(mult(rd(A,mult(B,B)),B),C) = mult(A,ld(B,C)),
inference(para_into,[status(thm),theory(equality)],[21,4]),
[iquote('para_into,21.1.1.2,3.1.1')] ).
cnf(56,plain,
mult(A,ld(mult(B,mult(A,A)),C)) = ld(mult(B,A),C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[23,5])]),
[iquote('para_from,23.1.1,5.1.1.2,flip.1')] ).
cnf(89,plain,
rd(mult(A,mult(B,C)),C) = mult(rd(A,B),mult(B,B)),
inference(para_into,[status(thm),theory(equality)],[25,8]),
[iquote('para_into,25.1.1.1.1,7.1.1')] ).
cnf(129,plain,
mult(A,ld(B,ld(mult(rd(A,mult(B,B)),B),C))) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[36,4])]),
[iquote('para_into,36.1.1,3.1.1,flip.1')] ).
cnf(166,plain,
ld(mult(A,mult(B,B)),C) = ld(B,ld(mult(A,B),C)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[56,5])]),
[iquote('para_from,56.1.1,5.1.1.2,flip.1')] ).
cnf(172,plain,
mult(rd(rd(A,mult(B,C)),B),mult(B,B)) = rd(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[89,8])]),
[iquote('para_into,89.1.1.1,7.1.1,flip.1')] ).
cnf(174,plain,
ld(mult(rd(A,mult(A,A)),A),B) = B,
inference(para_into,[status(thm),theory(equality)],[129,4]),
[iquote('para_into,129.1.1,3.1.1')] ).
cnf(180,plain,
rd(A,A) = mult(rd(B,mult(B,B)),B),
inference(para_from,[status(thm),theory(equality)],[174,15]),
[iquote('para_from,174.1.1,15.1.1.2')] ).
cnf(181,plain,
mult(rd(A,mult(A,A)),A) = rd(B,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[180])]),
[iquote('copy,180,flip.1')] ).
cnf(187,plain,
ld(rd(A,A),B) = B,
inference(para_from,[status(thm),theory(equality)],[181,174]),
[iquote('para_from,181.1.1,174.1.1.1')] ).
cnf(188,plain,
mult(rd(A,A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[181,36]),4]),
[iquote('para_from,181.1.1,36.1.1.1,demod,4')] ).
cnf(190,plain,
rd(rd(A,A),B) = rd(B,mult(B,B)),
inference(para_from,[status(thm),theory(equality)],[181,10]),
[iquote('para_from,181.1.1,9.1.1.1')] ).
cnf(191,plain,
ld(rd(A,mult(A,A)),rd(B,B)) = A,
inference(para_from,[status(thm),theory(equality)],[181,5]),
[iquote('para_from,181.1.1,5.1.1.2')] ).
cnf(193,plain,
rd(A,mult(A,A)) = rd(rd(B,B),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[190])]),
[iquote('copy,190,flip.1')] ).
cnf(194,plain,
mult(rd(rd(A,A),B),mult(B,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[188,89]),10])]),
[iquote('para_from,188.1.1,89.1.1.1,demod,10,flip.1')] ).
cnf(205,plain,
ld(rd(rd(A,A),B),rd(C,C)) = B,
inference(para_from,[status(thm),theory(equality)],[193,191]),
[iquote('para_from,193.1.1,191.1.1.1')] ).
cnf(210,plain,
mult(rd(rd(rd(A,A),B),B),mult(B,B)) = rd(B,B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[194,89])]),
[iquote('para_from,194.1.1,89.1.1.1,flip.1')] ).
cnf(240,plain,
ld(A,rd(B,B)) = ld(A,rd(C,C)),
inference(para_into,[status(thm),theory(equality)],[205,15]),
[iquote('para_into,204.1.1.1,15.1.1')] ).
cnf(261,plain,
ld(A,ld(rd(rd(B,B),A),C)) = C,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[210,166]),187,8])]),
[iquote('para_from,210.1.1,166.1.1.1,demod,187,8,flip.1')] ).
cnf(269,plain,
ld(A,A) = rd(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[261,240]),205]),
[iquote('para_into,261.1.1.2,240.1.1,demod,205')] ).
cnf(280,plain,
rd(A,rd(B,B)) = A,
inference(para_from,[status(thm),theory(equality)],[269,15]),
[iquote('para_from,269.1.1,15.1.1.2')] ).
cnf(283,plain,
mult(A,rd(B,B)) = A,
inference(para_from,[status(thm),theory(equality)],[269,4]),
[iquote('para_from,269.1.1,3.1.1.2')] ).
cnf(317,plain,
mult(rd(A,B),mult(B,B)) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[280,89]),283]),
[iquote('para_into,280.1.1,89.1.1,demod,283')] ).
cnf(319,plain,
mult(rd(A,mult(B,C)),B) = rd(A,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[172]),317]),
[iquote('back_demod,172,demod,317')] ).
cnf(333,plain,
mult(rd(A,B),C) = mult(A,ld(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[36]),319]),
[iquote('back_demod,36,demod,319')] ).
cnf(340,plain,
dollar_f1(rd(A,A)) != dollar_f1(rd(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[283,1]),333,4]),
[iquote('para_from,282.1.1,1.1.1,demod,333,4')] ).
cnf(341,plain,
$false,
inference(binary,[status(thm)],[340,2]),
[iquote('binary,340.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP658+1 : TPTP v8.1.0. Released v4.0.0.
% 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 05:04:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.92/2.11 ----- Otter 3.3f, August 2004 -----
% 1.92/2.11 The process was started by sandbox on n007.cluster.edu,
% 1.92/2.11 Wed Jul 27 05:04:31 2022
% 1.92/2.11 The command was "./otter". The process ID is 4296.
% 1.92/2.11
% 1.92/2.11 set(prolog_style_variables).
% 1.92/2.11 set(auto).
% 1.92/2.11 dependent: set(auto1).
% 1.92/2.11 dependent: set(process_input).
% 1.92/2.11 dependent: clear(print_kept).
% 1.92/2.11 dependent: clear(print_new_demod).
% 1.92/2.11 dependent: clear(print_back_demod).
% 1.92/2.11 dependent: clear(print_back_sub).
% 1.92/2.11 dependent: set(control_memory).
% 1.92/2.11 dependent: assign(max_mem, 12000).
% 1.92/2.11 dependent: assign(pick_given_ratio, 4).
% 1.92/2.11 dependent: assign(stats_level, 1).
% 1.92/2.11 dependent: assign(max_seconds, 10800).
% 1.92/2.11 clear(print_given).
% 1.92/2.11
% 1.92/2.11 formula_list(usable).
% 1.92/2.11 all A (A=A).
% 1.92/2.11 all B A (mult(A,ld(A,B))=B).
% 1.92/2.11 all B A (ld(A,mult(A,B))=B).
% 1.92/2.11 all B A (mult(rd(A,B),B)=A).
% 1.92/2.11 all B A (rd(mult(A,B),B)=A).
% 1.92/2.11 all C B A (mult(mult(A,mult(B,B)),C)=mult(mult(A,B),mult(B,C))).
% 1.92/2.11 -(exists X0 all X1 (mult(X1,X0)=X1&mult(X0,X1)=X1)).
% 1.92/2.11 end_of_list.
% 1.92/2.11
% 1.92/2.11 -------> usable clausifies to:
% 1.92/2.11
% 1.92/2.11 list(usable).
% 1.92/2.11 0 [] A=A.
% 1.92/2.11 0 [] mult(A,ld(A,B))=B.
% 1.92/2.11 0 [] ld(A,mult(A,B))=B.
% 1.92/2.11 0 [] mult(rd(A,B),B)=A.
% 1.92/2.11 0 [] rd(mult(A,B),B)=A.
% 1.92/2.11 0 [] mult(mult(A,mult(B,B)),C)=mult(mult(A,B),mult(B,C)).
% 1.92/2.11 0 [] mult($f1(X0),X0)!=$f1(X0)|mult(X0,$f1(X0))!=$f1(X0).
% 1.92/2.11 end_of_list.
% 1.92/2.11
% 1.92/2.11 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.92/2.11
% 1.92/2.11 This is a Horn set with equality. The strategy will be
% 1.92/2.11 Knuth-Bendix and hyper_res, with positive clauses in
% 1.92/2.11 sos and nonpositive clauses in usable.
% 1.92/2.11
% 1.92/2.11 dependent: set(knuth_bendix).
% 1.92/2.11 dependent: set(anl_eq).
% 1.92/2.11 dependent: set(para_from).
% 1.92/2.11 dependent: set(para_into).
% 1.92/2.11 dependent: clear(para_from_right).
% 1.92/2.11 dependent: clear(para_into_right).
% 1.92/2.11 dependent: set(para_from_vars).
% 1.92/2.11 dependent: set(eq_units_both_ways).
% 1.92/2.11 dependent: set(dynamic_demod_all).
% 1.92/2.11 dependent: set(dynamic_demod).
% 1.92/2.11 dependent: set(order_eq).
% 1.92/2.11 dependent: set(back_demod).
% 1.92/2.11 dependent: set(lrpo).
% 1.92/2.11 dependent: set(hyper_res).
% 1.92/2.11 dependent: clear(order_hyper).
% 1.92/2.11
% 1.92/2.11 ------------> process usable:
% 1.92/2.11 ** KEPT (pick-wt=14): 1 [] mult($f1(A),A)!=$f1(A)|mult(A,$f1(A))!=$f1(A).
% 1.92/2.11
% 1.92/2.11 ------------> process sos:
% 1.92/2.11 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.92/2.11 ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.92/2.11 ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.92/2.11 ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.92/2.11 ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.92/2.11 ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.92/2.11 ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.92/2.11 ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.92/2.11 ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.92/2.11 ** KEPT (pick-wt=15): 11 [] mult(mult(A,mult(B,B)),C)=mult(mult(A,B),mult(B,C)).
% 1.92/2.11 ---> New Demodulator: 12 [new_demod,11] mult(mult(A,mult(B,B)),C)=mult(mult(A,B),mult(B,C)).
% 1.92/2.11 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.92/2.11 >>>> Starting back demodulation with 4.
% 1.92/2.11 >>>> Starting back demodulation with 6.
% 1.92/2.11 >>>> Starting back demodulation with 8.
% 1.92/2.11 >>>> Starting back demodulation with 10.
% 1.92/2.11 >>>> Starting back demodulation with 12.
% 1.92/2.11
% 1.92/2.11 ======= end of input processing =======
% 1.92/2.11
% 1.92/2.11 =========== start of search ===========
% 1.92/2.11
% 1.92/2.11
% 1.92/2.11 Resetting weight limit to 15.
% 1.92/2.11
% 1.92/2.11
% 1.92/2.11 Resetting weight limit to 15.
% 1.92/2.11
% 1.92/2.11 sos_size=49
% 1.92/2.11
% 1.92/2.11
% 1.92/2.11 Resetting weight limit to 11.
% 1.92/2.11
% 1.92/2.11
% 1.92/2.11 Resetting weight limit to 11.
% 1.92/2.11
% 1.92/2.11 sos_size=72
% 1.92/2.11
% 1.92/2.11 -------- PROOF --------
% 1.92/2.11
% 1.92/2.11 ----> UNIT CONFLICT at 0.35 sec ----> 341 [binary,340.1,2.1] $F.
% 1.92/2.11
% 1.92/2.11 Length of proof is 30. Level of proof is 16.
% 1.92/2.11
% 1.92/2.11 ---------------- PROOF ----------------
% 1.92/2.11 % SZS status Theorem
% 1.92/2.11 % SZS output start Refutation
% See solution above
% 1.92/2.12 ------------ end of proof -------------
% 1.92/2.12
% 1.92/2.12
% 1.92/2.12 Search stopped by max_proofs option.
% 1.92/2.12
% 1.92/2.12
% 1.92/2.12 Search stopped by max_proofs option.
% 1.92/2.12
% 1.92/2.12 ============ end of search ============
% 1.92/2.12
% 1.92/2.12 -------------- statistics -------------
% 1.92/2.12 clauses given 73
% 1.92/2.12 clauses generated 5173
% 1.92/2.12 clauses kept 195
% 1.92/2.12 clauses forward subsumed 864
% 1.92/2.12 clauses back subsumed 2
% 1.92/2.12 Kbytes malloced 5859
% 1.92/2.12
% 1.92/2.12 ----------- times (seconds) -----------
% 1.92/2.12 user CPU time 0.35 (0 hr, 0 min, 0 sec)
% 1.92/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.12 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.92/2.12
% 1.92/2.12 That finishes the proof of the theorem.
% 1.92/2.12
% 1.92/2.12 Process 4296 finished Wed Jul 27 05:04:32 2022
% 1.92/2.12 Otter interrupted
% 1.92/2.12 PROOF FOUND
%------------------------------------------------------------------------------