%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO021-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 12:47:37 EDT 2022
% Result : Unsatisfiable 1.74s 1.95s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 2 RR)
% Number of literals : 7 ( 6 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(b,a) != multiply(a,b),
file('BOO021-1.p',unknown),
[] ).
cnf(3,axiom,
multiply(add(A,B),B) = B,
file('BOO021-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)),
file('BOO021-1.p',unknown),
[] ).
cnf(8,axiom,
add(multiply(A,B),B) = B,
file('BOO021-1.p',unknown),
[] ).
cnf(21,plain,
add(A,A) = A,
inference(para_into,[status(thm),theory(equality)],[8,3]),
[iquote('para_into,8.1.1.1,3.1.1')] ).
cnf(32,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[21,5]),21]),
[iquote('para_from,20.1.1,5.1.1.2,demod,21')] ).
cnf(33,plain,
$false,
inference(binary,[status(thm)],[32,1]),
[iquote('binary,32.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO021-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 02:40:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.74/1.95 ----- Otter 3.3f, August 2004 -----
% 1.74/1.95 The process was started by sandbox2 on n018.cluster.edu,
% 1.74/1.95 Wed Jul 27 02:40:01 2022
% 1.74/1.95 The command was "./otter". The process ID is 4676.
% 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 list(usable).
% 1.74/1.95 0 [] A=A.
% 1.74/1.95 0 [] multiply(add(X,Y),Y)=Y.
% 1.74/1.95 0 [] multiply(X,add(Y,Z))=add(multiply(Y,X),multiply(Z,X)).
% 1.74/1.95 0 [] add(X,inverse(X))=n1.
% 1.74/1.95 0 [] add(multiply(X,Y),Y)=Y.
% 1.74/1.95 0 [] add(X,multiply(Y,Z))=multiply(add(Y,X),add(Z,X)).
% 1.74/1.95 0 [] multiply(X,inverse(X))=n0.
% 1.74/1.95 0 [] multiply(b,a)!=multiply(a,b).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.95
% 1.74/1.95 All clauses are units, and equality is present; the
% 1.74/1.95 strategy will be Knuth-Bendix with positive clauses in sos.
% 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
% 1.74/1.95 ------------> process usable:
% 1.74/1.95 ** KEPT (pick-wt=7): 1 [] multiply(b,a)!=multiply(a,b).
% 1.74/1.95
% 1.74/1.95 ------------> process sos:
% 1.74/1.95 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.74/1.95 ** KEPT (pick-wt=7): 3 [] multiply(add(A,B),B)=B.
% 1.74/1.95 ---> New Demodulator: 4 [new_demod,3] multiply(add(A,B),B)=B.
% 1.74/1.95 ** KEPT (pick-wt=13): 5 [] multiply(A,add(B,C))=add(multiply(B,A),multiply(C,A)).
% 1.74/1.95 ** KEPT (pick-wt=6): 6 [] add(A,inverse(A))=n1.
% 1.74/1.95 ---> New Demodulator: 7 [new_demod,6] add(A,inverse(A))=n1.
% 1.74/1.95 ** KEPT (pick-wt=7): 8 [] add(multiply(A,B),B)=B.
% 1.74/1.95 ---> New Demodulator: 9 [new_demod,8] add(multiply(A,B),B)=B.
% 1.74/1.95 ** KEPT (pick-wt=13): 11 [copy,10,flip.1] multiply(add(A,B),add(C,B))=add(B,multiply(A,C)).
% 1.74/1.95 ---> New Demodulator: 12 [new_demod,11] multiply(add(A,B),add(C,B))=add(B,multiply(A,C)).
% 1.74/1.95 ** KEPT (pick-wt=6): 13 [] multiply(A,inverse(A))=n0.
% 1.74/1.95 ---> New Demodulator: 14 [new_demod,13] multiply(A,inverse(A))=n0.
% 1.74/1.95 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.74/1.95 >>>> Starting back demodulation with 4.
% 1.74/1.95 ** KEPT (pick-wt=13): 15 [copy,5,flip.1] add(multiply(A,B),multiply(C,B))=multiply(B,add(A,C)).
% 1.74/1.95 >>>> Starting back demodulation with 7.
% 1.74/1.95 >>>> Starting back demodulation with 9.
% 1.74/1.95 >>>> Starting back demodulation with 12.
% 1.74/1.95 >>>> Starting back demodulation with 14.
% 1.74/1.95 Following clause subsumed by 5 during input processing: 0 [copy,15,flip.1] multiply(A,add(B,C))=add(multiply(B,A),multiply(C,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 0.00 sec ----> 33 [binary,32.1,1.1] $F.
% 1.74/1.95
% 1.74/1.95 Length of proof is 2. Level of proof is 2.
% 1.74/1.95
% 1.74/1.95 ---------------- PROOF ----------------
% 1.74/1.95 % SZS status Unsatisfiable
% 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 7
% 1.74/1.95 clauses generated 22
% 1.74/1.95 clauses kept 20
% 1.74/1.95 clauses forward subsumed 17
% 1.74/1.95 clauses back subsumed 0
% 1.74/1.95 Kbytes malloced 976
% 1.74/1.95
% 1.74/1.95 ----------- times (seconds) -----------
% 1.74/1.95 user CPU time 0.00 (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 4676 finished Wed Jul 27 02:40:02 2022
% 1.74/1.95 Otter interrupted
% 1.74/1.95 PROOF FOUND
%------------------------------------------------------------------------------