TSTP Solution File: GRP402-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:56:56 EDT 2022
% Result : Unsatisfiable 3.05s 3.22s
% Output : Refutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 29 ( 18 unt; 0 nHn; 11 RR)
% Number of literals : 42 ( 41 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(A,B) != multiply(C,B)
| A = C ),
file('GRP402-1.p',unknown),
[] ).
cnf(2,axiom,
( multiply(A,B) != multiply(A,C)
| B = C ),
file('GRP402-1.p',unknown),
[] ).
cnf(3,axiom,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('GRP402-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP402-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = multiply(B,multiply(A,commutator(A,B))),
file('GRP402-1.p',unknown),
[] ).
cnf(8,plain,
multiply(A,multiply(B,commutator(B,A))) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,axiom,
multiply(commutator(A,B),C) = multiply(C,commutator(A,B)),
file('GRP402-1.p',unknown),
[] ).
cnf(11,plain,
multiply(A,commutator(B,C)) = multiply(commutator(B,C),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(19,plain,
multiply(A,commutator(A,A)) = A,
inference(hyper,[status(thm)],[8,2]),
[iquote('hyper,8,2')] ).
cnf(32,plain,
( multiply(A,B) != multiply(B,C)
| multiply(A,commutator(A,B)) = C ),
inference(para_from,[status(thm),theory(equality)],[8,2]),
[iquote('para_from,8.1.1,2.1.1')] ).
cnf(38,plain,
( A = B
| multiply(C,B) != multiply(C,A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,2]),19]),
[iquote('para_into,18.1.1,2.2.1,demod,19')] ).
cnf(40,plain,
multiply(A,multiply(commutator(A,A),B)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[19,6])]),
[iquote('para_from,18.1.1,5.1.1.1,flip.1')] ).
cnf(42,plain,
( multiply(A,B) != A
| commutator(A,A) = B ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[19,2])]),
[iquote('para_from,18.1.1,2.1.1,flip.1')] ).
cnf(74,plain,
multiply(A,multiply(commutator(B,C),D)) = multiply(commutator(B,C),multiply(A,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[10,6]),6]),
[iquote('para_from,10.1.1,5.1.1.1,demod,6')] ).
cnf(77,plain,
multiply(commutator(A,B),multiply(C,D)) = multiply(C,multiply(commutator(A,B),D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[74])]),
[iquote('copy,74,flip.1')] ).
cnf(183,plain,
multiply(commutator(A,A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,19])]),
[iquote('para_into,11.1.1,18.1.1,flip.1')] ).
cnf(207,plain,
( A = B
| multiply(commutator(B,B),A) != B ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[183,38])]),
[iquote('para_from,183.1.1,38.2.1,flip.2')] ).
cnf(210,plain,
( multiply(A,B) != B
| commutator(B,B) = A ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[183,1])]),
[iquote('para_from,183.1.1,1.1.1,flip.1')] ).
cnf(483,plain,
( A != multiply(B,C)
| D = C
| multiply(commutator(A,A),multiply(B,D)) != A ),
inference(para_from,[status(thm),theory(equality)],[207,2]),
[iquote('para_from,207.1.1,2.1.1')] ).
cnf(638,plain,
multiply(commutator(A,A),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[40,38])]),
[iquote('hyper,40,38,flip.1')] ).
cnf(662,plain,
( A != multiply(B,C)
| D = C
| multiply(B,D) != A ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[483]),638]),
[iquote('back_demod,483,demod,638')] ).
cnf(764,plain,
commutator(A,A) = commutator(B,B),
inference(hyper,[status(thm)],[638,210]),
[iquote('hyper,637,210')] ).
cnf(803,plain,
( multiply(A,B) != A
| commutator(C,C) = B ),
inference(para_from,[status(thm),theory(equality)],[764,42]),
[iquote('para_from,764.1.1,42.2.1')] ).
cnf(2694,plain,
multiply(A,commutator(A,commutator(B,C))) = A,
inference(hyper,[status(thm)],[32,11]),
[iquote('hyper,32,11')] ).
cnf(2696,plain,
commutator(A,A) = commutator(B,commutator(C,D)),
inference(hyper,[status(thm)],[2694,803]),
[iquote('hyper,2694,803')] ).
cnf(2710,plain,
( A = commutator(B,commutator(C,D))
| multiply(E,A) != E ),
inference(para_into,[status(thm),theory(equality)],[2696,803]),
[iquote('para_into,2696.1.1,803.2.1')] ).
cnf(2801,plain,
multiply(A,commutator(commutator(B,C),A)) = A,
inference(hyper,[status(thm)],[662,8,77]),
[iquote('hyper,662,8,77')] ).
cnf(2807,plain,
commutator(commutator(A,B),C) = commutator(D,commutator(E,F)),
inference(hyper,[status(thm)],[2801,2710]),
[iquote('hyper,2801,2710')] ).
cnf(2808,plain,
$false,
inference(binary,[status(thm)],[2807,3]),
[iquote('binary,2807.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n012.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 05:02:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.05/3.22 ----- Otter 3.3f, August 2004 -----
% 3.05/3.22 The process was started by sandbox on n012.cluster.edu,
% 3.05/3.22 Wed Jul 27 05:02:35 2022
% 3.05/3.22 The command was "./otter". The process ID is 27972.
% 3.05/3.22
% 3.05/3.22 set(prolog_style_variables).
% 3.05/3.22 set(auto).
% 3.05/3.22 dependent: set(auto1).
% 3.05/3.22 dependent: set(process_input).
% 3.05/3.22 dependent: clear(print_kept).
% 3.05/3.22 dependent: clear(print_new_demod).
% 3.05/3.22 dependent: clear(print_back_demod).
% 3.05/3.22 dependent: clear(print_back_sub).
% 3.05/3.22 dependent: set(control_memory).
% 3.05/3.22 dependent: assign(max_mem, 12000).
% 3.05/3.22 dependent: assign(pick_given_ratio, 4).
% 3.05/3.22 dependent: assign(stats_level, 1).
% 3.05/3.22 dependent: assign(max_seconds, 10800).
% 3.05/3.22 clear(print_given).
% 3.05/3.22
% 3.05/3.22 list(usable).
% 3.05/3.22 0 [] A=A.
% 3.05/3.22 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 3.05/3.22 0 [] multiply(A,B)!=multiply(C,B)|A=C.
% 3.05/3.22 0 [] multiply(A,B)!=multiply(A,C)|B=C.
% 3.05/3.22 0 [] multiply(A,B)=multiply(B,multiply(A,commutator(A,B))).
% 3.05/3.22 0 [] multiply(commutator(A,B),C)=multiply(C,commutator(A,B)).
% 3.05/3.22 0 [] commutator(commutator(a,b),c)!=commutator(a,commutator(b,c)).
% 3.05/3.22 end_of_list.
% 3.05/3.22
% 3.05/3.22 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 3.05/3.22
% 3.05/3.22 This is a Horn set with equality. The strategy will be
% 3.05/3.22 Knuth-Bendix and hyper_res, with positive clauses in
% 3.05/3.22 sos and nonpositive clauses in usable.
% 3.05/3.22
% 3.05/3.22 dependent: set(knuth_bendix).
% 3.05/3.22 dependent: set(anl_eq).
% 3.05/3.22 dependent: set(para_from).
% 3.05/3.22 dependent: set(para_into).
% 3.05/3.22 dependent: clear(para_from_right).
% 3.05/3.22 dependent: clear(para_into_right).
% 3.05/3.22 dependent: set(para_from_vars).
% 3.05/3.22 dependent: set(eq_units_both_ways).
% 3.05/3.22 dependent: set(dynamic_demod_all).
% 3.05/3.22 dependent: set(dynamic_demod).
% 3.05/3.22 dependent: set(order_eq).
% 3.05/3.22 dependent: set(back_demod).
% 3.05/3.22 dependent: set(lrpo).
% 3.05/3.22 dependent: set(hyper_res).
% 3.05/3.22 dependent: clear(order_hyper).
% 3.05/3.22
% 3.05/3.22 ------------> process usable:
% 3.05/3.22 ** KEPT (pick-wt=10): 1 [] multiply(A,B)!=multiply(C,B)|A=C.
% 3.05/3.22 ** KEPT (pick-wt=10): 2 [] multiply(A,B)!=multiply(A,C)|B=C.
% 3.05/3.22 ** KEPT (pick-wt=11): 3 [] commutator(commutator(a,b),c)!=commutator(a,commutator(b,c)).
% 3.05/3.22
% 3.05/3.22 ------------> process sos:
% 3.05/3.22 ** KEPT (pick-wt=3): 4 [] A=A.
% 3.05/3.22 ** KEPT (pick-wt=11): 5 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 3.05/3.22 ---> New Demodulator: 6 [new_demod,5] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 3.05/3.22 ** KEPT (pick-wt=11): 8 [copy,7,flip.1] multiply(A,multiply(B,commutator(B,A)))=multiply(B,A).
% 3.05/3.22 ---> New Demodulator: 9 [new_demod,8] multiply(A,multiply(B,commutator(B,A)))=multiply(B,A).
% 3.05/3.22 ** KEPT (pick-wt=11): 10 [] multiply(commutator(A,B),C)=multiply(C,commutator(A,B)).
% 3.05/3.22 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 3.05/3.22 >>>> Starting back demodulation with 6.
% 3.05/3.22 >>>> Starting back demodulation with 9.
% 3.05/3.22 ** KEPT (pick-wt=11): 11 [copy,10,flip.1] multiply(A,commutator(B,C))=multiply(commutator(B,C),A).
% 3.05/3.22 Following clause subsumed by 10 during input processing: 0 [copy,11,flip.1] multiply(commutator(A,B),C)=multiply(C,commutator(A,B)).
% 3.05/3.22
% 3.05/3.22 ======= end of input processing =======
% 3.05/3.22
% 3.05/3.22 =========== start of search ===========
% 3.05/3.22
% 3.05/3.22
% 3.05/3.22 Resetting weight limit to 12.
% 3.05/3.22
% 3.05/3.22
% 3.05/3.22 Resetting weight limit to 12.
% 3.05/3.22
% 3.05/3.22 sos_size=1794
% 3.05/3.22
% 3.05/3.22 -------- PROOF --------
% 3.05/3.22
% 3.05/3.22 ----> UNIT CONFLICT at 1.30 sec ----> 2808 [binary,2807.1,3.1] $F.
% 3.05/3.22
% 3.05/3.22 Length of proof is 22. Level of proof is 9.
% 3.05/3.22
% 3.05/3.22 ---------------- PROOF ----------------
% 3.05/3.22 % SZS status Unsatisfiable
% 3.05/3.22 % SZS output start Refutation
% See solution above
% 3.05/3.22 ------------ end of proof -------------
% 3.05/3.22
% 3.05/3.22
% 3.05/3.22 Search stopped by max_proofs option.
% 3.05/3.22
% 3.05/3.22
% 3.05/3.22 Search stopped by max_proofs option.
% 3.05/3.22
% 3.05/3.22 ============ end of search ============
% 3.05/3.22
% 3.05/3.22 -------------- statistics -------------
% 3.05/3.22 clauses given 310
% 3.05/3.22 clauses generated 121701
% 3.05/3.22 clauses kept 2672
% 3.05/3.22 clauses forward subsumed 36847
% 3.05/3.22 clauses back subsumed 283
% 3.05/3.22 Kbytes malloced 4882
% 3.05/3.22
% 3.05/3.22 ----------- times (seconds) -----------
% 3.05/3.22 user CPU time 1.30 (0 hr, 0 min, 1 sec)
% 3.05/3.22 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.05/3.22 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.05/3.22
% 3.05/3.22 That finishes the proof of the theorem.
% 3.05/3.22
% 3.05/3.22 Process 27972 finished Wed Jul 27 05:02:38 2022
% 3.05/3.22 Otter interrupted
% 3.05/3.22 PROOF FOUND
%------------------------------------------------------------------------------