TSTP Solution File: GRP001-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:55:48 EDT 2022
% Result : Unsatisfiable 1.69s 1.90s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 6 RR)
% Number of literals : 12 ( 11 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(b,a) != c,
file('GRP001-2.p',unknown),
[] ).
cnf(4,axiom,
multiply(identity,A) = A,
file('GRP001-2.p',unknown),
[] ).
cnf(7,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP001-2.p',unknown),
[] ).
cnf(10,axiom,
multiply(A,identity) = A,
file('GRP001-2.p',unknown),
[] ).
cnf(13,axiom,
multiply(A,A) = identity,
file('GRP001-2.p',unknown),
[] ).
cnf(15,axiom,
multiply(a,b) = c,
file('GRP001-2.p',unknown),
[] ).
cnf(19,plain,
multiply(c,A) = multiply(a,multiply(b,A)),
inference(para_into,[status(thm),theory(equality)],[7,15]),
[iquote('para_into,7.1.1.1,15.1.1')] ).
cnf(21,plain,
multiply(A,multiply(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,13]),4])]),
[iquote('para_into,7.1.1.1,13.1.1,demod,4,flip.1')] ).
cnf(37,plain,
multiply(a,multiply(b,c)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,13])]),
[iquote('para_into,19.1.1,13.1.1,flip.1')] ).
cnf(39,plain,
multiply(b,c) = a,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[37,21]),10])]),
[iquote('para_from,37.1.1,21.1.1.2,demod,10,flip.1')] ).
cnf(41,plain,
multiply(b,a) = c,
inference(para_from,[status(thm),theory(equality)],[39,21]),
[iquote('para_from,39.1.1,21.1.1.2')] ).
cnf(43,plain,
$false,
inference(binary,[status(thm)],[41,1]),
[iquote('binary,41.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:12:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.69/1.90 ----- Otter 3.3f, August 2004 -----
% 1.69/1.90 The process was started by sandbox on n003.cluster.edu,
% 1.69/1.90 Wed Jul 27 05:12:41 2022
% 1.69/1.90 The command was "./otter". The process ID is 28516.
% 1.69/1.90
% 1.69/1.90 set(prolog_style_variables).
% 1.69/1.90 set(auto).
% 1.69/1.90 dependent: set(auto1).
% 1.69/1.90 dependent: set(process_input).
% 1.69/1.90 dependent: clear(print_kept).
% 1.69/1.90 dependent: clear(print_new_demod).
% 1.69/1.90 dependent: clear(print_back_demod).
% 1.69/1.90 dependent: clear(print_back_sub).
% 1.69/1.90 dependent: set(control_memory).
% 1.69/1.90 dependent: assign(max_mem, 12000).
% 1.69/1.90 dependent: assign(pick_given_ratio, 4).
% 1.69/1.90 dependent: assign(stats_level, 1).
% 1.69/1.90 dependent: assign(max_seconds, 10800).
% 1.69/1.90 clear(print_given).
% 1.69/1.90
% 1.69/1.90 list(usable).
% 1.69/1.90 0 [] A=A.
% 1.69/1.90 0 [] multiply(identity,X)=X.
% 1.69/1.90 0 [] multiply(inverse(X),X)=identity.
% 1.69/1.90 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.69/1.90 0 [] multiply(X,identity)=X.
% 1.69/1.90 0 [] multiply(X,inverse(X))=identity.
% 1.69/1.90 0 [] multiply(X,X)=identity.
% 1.69/1.90 0 [] multiply(a,b)=c.
% 1.69/1.90 0 [] multiply(b,a)!=c.
% 1.69/1.90 end_of_list.
% 1.69/1.90
% 1.69/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.69/1.90
% 1.69/1.90 All clauses are units, and equality is present; the
% 1.69/1.90 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.69/1.90
% 1.69/1.90 dependent: set(knuth_bendix).
% 1.69/1.90 dependent: set(anl_eq).
% 1.69/1.90 dependent: set(para_from).
% 1.69/1.90 dependent: set(para_into).
% 1.69/1.90 dependent: clear(para_from_right).
% 1.69/1.90 dependent: clear(para_into_right).
% 1.69/1.90 dependent: set(para_from_vars).
% 1.69/1.90 dependent: set(eq_units_both_ways).
% 1.69/1.90 dependent: set(dynamic_demod_all).
% 1.69/1.90 dependent: set(dynamic_demod).
% 1.69/1.90 dependent: set(order_eq).
% 1.69/1.90 dependent: set(back_demod).
% 1.69/1.90 dependent: set(lrpo).
% 1.69/1.90
% 1.69/1.90 ------------> process usable:
% 1.69/1.90 ** KEPT (pick-wt=5): 1 [] multiply(b,a)!=c.
% 1.69/1.90
% 1.69/1.90 ------------> process sos:
% 1.69/1.90 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.69/1.90 ** KEPT (pick-wt=5): 3 [] multiply(identity,A)=A.
% 1.69/1.90 ---> New Demodulator: 4 [new_demod,3] multiply(identity,A)=A.
% 1.69/1.90 ** KEPT (pick-wt=6): 5 [] multiply(inverse(A),A)=identity.
% 1.69/1.90 ---> New Demodulator: 6 [new_demod,5] multiply(inverse(A),A)=identity.
% 1.69/1.90 ** KEPT (pick-wt=11): 7 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.69/1.90 ---> New Demodulator: 8 [new_demod,7] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.69/1.90 ** KEPT (pick-wt=5): 9 [] multiply(A,identity)=A.
% 1.69/1.90 ---> New Demodulator: 10 [new_demod,9] multiply(A,identity)=A.
% 1.69/1.90 ** KEPT (pick-wt=6): 11 [] multiply(A,inverse(A))=identity.
% 1.69/1.90 ---> New Demodulator: 12 [new_demod,11] multiply(A,inverse(A))=identity.
% 1.69/1.90 ** KEPT (pick-wt=5): 13 [] multiply(A,A)=identity.
% 1.69/1.90 ---> New Demodulator: 14 [new_demod,13] multiply(A,A)=identity.
% 1.69/1.90 ** KEPT (pick-wt=5): 15 [] multiply(a,b)=c.
% 1.69/1.90 ---> New Demodulator: 16 [new_demod,15] multiply(a,b)=c.
% 1.69/1.90 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.69/1.90 >>>> Starting back demodulation with 4.
% 1.69/1.90 >>>> Starting back demodulation with 6.
% 1.69/1.90 >>>> Starting back demodulation with 8.
% 1.69/1.90 >>>> Starting back demodulation with 10.
% 1.69/1.90 >>>> Starting back demodulation with 12.
% 1.69/1.90 >>>> Starting back demodulation with 14.
% 1.69/1.90 >>>> Starting back demodulation with 16.
% 1.69/1.90
% 1.69/1.90 ======= end of input processing =======
% 1.69/1.90
% 1.69/1.90 =========== start of search ===========
% 1.69/1.90
% 1.69/1.90 -------- PROOF --------
% 1.69/1.90
% 1.69/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 43 [binary,41.1,1.1] $F.
% 1.69/1.90
% 1.69/1.90 Length of proof is 5. Level of proof is 4.
% 1.69/1.90
% 1.69/1.90 ---------------- PROOF ----------------
% 1.69/1.90 % SZS status Unsatisfiable
% 1.69/1.90 % SZS output start Refutation
% See solution above
% 1.69/1.90 ------------ end of proof -------------
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90 ============ end of search ============
% 1.69/1.90
% 1.69/1.90 -------------- statistics -------------
% 1.69/1.90 clauses given 15
% 1.69/1.90 clauses generated 81
% 1.69/1.90 clauses kept 22
% 1.69/1.90 clauses forward subsumed 76
% 1.69/1.90 clauses back subsumed 0
% 1.69/1.90 Kbytes malloced 976
% 1.69/1.90
% 1.69/1.90 ----------- times (seconds) -----------
% 1.69/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.69/1.90
% 1.69/1.90 That finishes the proof of the theorem.
% 1.69/1.90
% 1.69/1.90 Process 28516 finished Wed Jul 27 05:12:43 2022
% 1.69/1.90 Otter interrupted
% 1.69/1.90 PROOF FOUND
%------------------------------------------------------------------------------