%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG006-1 : TPTP v8.1.0. Released v1.0.0.
% 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 13:12:01 EDT 2022
% Result : Unsatisfiable 1.99s 2.21s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of clauses : 34 ( 26 unt; 0 nHn; 23 RR)
% Number of literals : 54 ( 7 equ; 21 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(C,D,F)
| sum(A,E,F) ),
file('RNG006-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG006-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('RNG006-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ product(A,F,G)
| sum(C,E,G) ),
file('RNG006-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(D,B,E)
| ~ sum(A,D,F)
| ~ sum(C,E,G)
| product(F,B,G) ),
file('RNG006-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('RNG006-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('RNG006-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(A,B,C)
| product(additive_inverse(A),B,additive_inverse(C)) ),
file('RNG006-1.p',unknown),
[] ).
cnf(15,axiom,
~ product(a,bS_Ic,aPb_S_IaPc),
file('RNG006-1.p',unknown),
[] ).
cnf(17,axiom,
sum(additive_identity,A,A),
file('RNG006-1.p',unknown),
[] ).
cnf(18,axiom,
sum(A,additive_identity,A),
file('RNG006-1.p',unknown),
[] ).
cnf(19,axiom,
product(A,B,multiply(A,B)),
file('RNG006-1.p',unknown),
[] ).
cnf(20,axiom,
sum(A,B,add(A,B)),
file('RNG006-1.p',unknown),
[] ).
cnf(21,axiom,
sum(additive_inverse(A),A,additive_identity),
file('RNG006-1.p',unknown),
[] ).
cnf(22,axiom,
sum(A,additive_inverse(A),additive_identity),
file('RNG006-1.p',unknown),
[] ).
cnf(23,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('RNG006-1.p',unknown),
[] ).
cnf(24,axiom,
product(a,b,aPb),
file('RNG006-1.p',unknown),
[] ).
cnf(25,axiom,
product(a,c,aPc),
file('RNG006-1.p',unknown),
[] ).
cnf(26,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('RNG006-1.p',unknown),
[] ).
cnf(41,plain,
product(additive_inverse(a),c,additive_inverse(aPc)),
inference(hyper,[status(thm)],[25,13]),
[iquote('hyper,25,13')] ).
cnf(50,plain,
product(additive_inverse(A),B,additive_inverse(multiply(A,B))),
inference(hyper,[status(thm)],[19,13]),
[iquote('hyper,19,13')] ).
cnf(119,plain,
sum(bS_Ic,c,b),
inference(hyper,[status(thm)],[23,2,21,18]),
[iquote('hyper,23,2,21,18')] ).
cnf(134,plain,
add(additive_inverse(A),A) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,10,21])]),
[iquote('hyper,20,10,21,flip.1')] ).
cnf(138,plain,
add(additive_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,10,17])]),
[iquote('hyper,20,10,17,flip.1')] ).
cnf(198,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[20,3]),
[iquote('hyper,20,3')] ).
cnf(228,plain,
sum(multiply(a,bS_Ic),aPc,aPb),
inference(hyper,[status(thm)],[119,6,19,25,24]),
[iquote('hyper,119,6,19,25,24')] ).
cnf(276,plain,
sum(additive_inverse(aPc),aPb,aPb_S_IaPc),
inference(hyper,[status(thm)],[26,3]),
[iquote('hyper,26,3')] ).
cnf(449,plain,
add(additive_inverse(aPc),aPb) = aPb_S_IaPc,
inference(hyper,[status(thm)],[276,10,20]),
[iquote('hyper,276,10,20')] ).
cnf(818,plain,
additive_inverse(aPc) = multiply(additive_inverse(a),c),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[41,11,19])]),
[iquote('hyper,41,11,19,flip.1')] ).
cnf(849,plain,
add(multiply(additive_inverse(a),c),aPb) = aPb_S_IaPc,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[449]),818]),
[iquote('back_demod,449,demod,818')] ).
cnf(1671,plain,
sum(multiply(a,bS_Ic),additive_identity,aPb_S_IaPc),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[228,1,22,198]),818,849]),
[iquote('hyper,228,1,22,198,demod,818,849')] ).
cnf(3228,plain,
product(additive_identity,A,additive_identity),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[50,9,19,198,22]),134]),
[iquote('hyper,50,9,19,198,22,demod,134')] ).
cnf(3256,plain,
product(a,bS_Ic,aPb_S_IaPc),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1671,9,19,3228,198]),138]),
[iquote('hyper,1671,9,19,3228,198,demod,138')] ).
cnf(3257,plain,
$false,
inference(binary,[status(thm)],[3256,15]),
[iquote('binary,3256.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : RNG006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 02:08:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.91 ----- Otter 3.3f, August 2004 -----
% 1.68/1.91 The process was started by sandbox on n012.cluster.edu,
% 1.68/1.91 Wed Jul 27 02:08:05 2022
% 1.68/1.91 The command was "./otter". The process ID is 25771.
% 1.68/1.91
% 1.68/1.91 set(prolog_style_variables).
% 1.68/1.91 set(auto).
% 1.68/1.91 dependent: set(auto1).
% 1.68/1.91 dependent: set(process_input).
% 1.68/1.91 dependent: clear(print_kept).
% 1.68/1.91 dependent: clear(print_new_demod).
% 1.68/1.91 dependent: clear(print_back_demod).
% 1.68/1.91 dependent: clear(print_back_sub).
% 1.68/1.91 dependent: set(control_memory).
% 1.68/1.91 dependent: assign(max_mem, 12000).
% 1.68/1.91 dependent: assign(pick_given_ratio, 4).
% 1.68/1.91 dependent: assign(stats_level, 1).
% 1.68/1.91 dependent: assign(max_seconds, 10800).
% 1.68/1.91 clear(print_given).
% 1.68/1.91
% 1.68/1.91 list(usable).
% 1.68/1.91 0 [] A=A.
% 1.68/1.91 0 [] sum(additive_identity,X,X).
% 1.68/1.91 0 [] sum(X,additive_identity,X).
% 1.68/1.91 0 [] product(X,Y,multiply(X,Y)).
% 1.68/1.91 0 [] sum(X,Y,add(X,Y)).
% 1.68/1.91 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.68/1.91 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.68/1.91 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.68/1.91 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.68/1.91 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.68/1.91 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.68/1.91 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.68/1.91 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.68/1.91 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.68/1.91 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.68/1.91 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.68/1.91 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.68/1.91 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.68/1.91 0 [] -product(A,B,C)|product(A,additive_inverse(B),additive_inverse(C)).
% 1.68/1.91 0 [] -product(A,B,C)|product(additive_inverse(A),B,additive_inverse(C)).
% 1.68/1.91 0 [] -product(A,B,C)|product(additive_inverse(A),additive_inverse(B),C).
% 1.68/1.91 0 [] sum(b,additive_inverse(c),bS_Ic).
% 1.68/1.91 0 [] product(a,b,aPb).
% 1.68/1.91 0 [] product(a,c,aPc).
% 1.68/1.91 0 [] sum(aPb,additive_inverse(aPc),aPb_S_IaPc).
% 1.68/1.91 0 [] -product(a,bS_Ic,aPb_S_IaPc).
% 1.68/1.91 end_of_list.
% 1.68/1.91
% 1.68/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.68/1.91
% 1.68/1.91 This is a Horn set with equality. The strategy will be
% 1.68/1.91 Knuth-Bendix and hyper_res, with positive clauses in
% 1.68/1.91 sos and nonpositive clauses in usable.
% 1.68/1.91
% 1.68/1.91 dependent: set(knuth_bendix).
% 1.68/1.91 dependent: set(anl_eq).
% 1.68/1.91 dependent: set(para_from).
% 1.68/1.91 dependent: set(para_into).
% 1.68/1.91 dependent: clear(para_from_right).
% 1.68/1.91 dependent: clear(para_into_right).
% 1.68/1.91 dependent: set(para_from_vars).
% 1.68/1.91 dependent: set(eq_units_both_ways).
% 1.68/1.91 dependent: set(dynamic_demod_all).
% 1.68/1.91 dependent: set(dynamic_demod).
% 1.68/1.91 dependent: set(order_eq).
% 1.68/1.91 dependent: set(back_demod).
% 1.68/1.91 dependent: set(lrpo).
% 1.68/1.91 dependent: set(hyper_res).
% 1.68/1.91 dependent: clear(order_hyper).
% 1.68/1.91
% 1.68/1.91 ------------> process usable:
% 1.68/1.91 ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.68/1.91 ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.68/1.91 ** KEPT (pick-wt=8): 3 [] -sum(A,B,C)|sum(B,A,C).
% 1.68/1.91 ** KEPT (pick-wt=16): 4 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.68/1.91 ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.68/1.91 ** KEPT (pick-wt=20): 6 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 1.68/1.91 ** KEPT (pick-wt=20): 7 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 1.68/1.91 ** KEPT (pick-wt=20): 8 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 1.68/1.91 ** KEPT (pick-wt=20): 9 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 1.68/1.91 ** KEPT (pick-wt=11): 10 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.68/1.91 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.68/1.91 ** KEPT (pick-wt=10): 12 [] -product(A,B,C)|product(A,additive_inverse(B),additive_inverse(C)).
% 1.68/1.91 ** KEPT (pick-wt=10): 13 [] -product(A,B,C)|product(additive_inverse(A),B,additive_inverse(C)).
% 1.68/1.91 ** KEPT (pick-wt=10): 14 [] -product(A,B,C)|product(additive_inverse(A),additive_inverse(B),C).
% 1.68/1.91 ** KEPT (pick-wt=4): 15 [] -product(a,bS_Ic,aPb_S_IaPc).
% 1.68/1.91
% 1.68/1.91 ------------> process sos:
% 1.68/1.91 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.68/1.91 ** KEPT (pick-wt=4): 17 [] sum(additive_identity,A,A).
% 1.99/2.21 ** KEPT (pick-wt=4): 18 [] sum(A,additive_identity,A).
% 1.99/2.21 ** KEPT (pick-wt=6): 19 [] product(A,B,multiply(A,B)).
% 1.99/2.21 ** KEPT (pick-wt=6): 20 [] sum(A,B,add(A,B)).
% 1.99/2.21 ** KEPT (pick-wt=5): 21 [] sum(additive_inverse(A),A,additive_identity).
% 1.99/2.21 ** KEPT (pick-wt=5): 22 [] sum(A,additive_inverse(A),additive_identity).
% 1.99/2.21 ** KEPT (pick-wt=5): 23 [] sum(b,additive_inverse(c),bS_Ic).
% 1.99/2.21 ** KEPT (pick-wt=4): 24 [] product(a,b,aPb).
% 1.99/2.21 ** KEPT (pick-wt=4): 25 [] product(a,c,aPc).
% 1.99/2.21 ** KEPT (pick-wt=5): 26 [] sum(aPb,additive_inverse(aPc),aPb_S_IaPc).
% 1.99/2.21 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 1.99/2.21
% 1.99/2.21 ======= end of input processing =======
% 1.99/2.21
% 1.99/2.21 =========== start of search ===========
% 1.99/2.21
% 1.99/2.21
% 1.99/2.21 Resetting weight limit to 8.
% 1.99/2.21
% 1.99/2.21
% 1.99/2.21 Resetting weight limit to 8.
% 1.99/2.21
% 1.99/2.21 sos_size=2341
% 1.99/2.21
% 1.99/2.21 -------- PROOF --------
% 1.99/2.21
% 1.99/2.21 ----> UNIT CONFLICT at 0.30 sec ----> 3257 [binary,3256.1,15.1] $F.
% 1.99/2.21
% 1.99/2.21 Length of proof is 14. Level of proof is 5.
% 1.99/2.21
% 1.99/2.21 ---------------- PROOF ----------------
% 1.99/2.21 % SZS status Unsatisfiable
% 1.99/2.21 % SZS output start Refutation
% See solution above
% 1.99/2.21 ------------ end of proof -------------
% 1.99/2.21
% 1.99/2.21
% 1.99/2.21 Search stopped by max_proofs option.
% 1.99/2.21
% 1.99/2.21
% 1.99/2.21 Search stopped by max_proofs option.
% 1.99/2.21
% 1.99/2.21 ============ end of search ============
% 1.99/2.21
% 1.99/2.21 -------------- statistics -------------
% 1.99/2.21 clauses given 113
% 1.99/2.21 clauses generated 25070
% 1.99/2.21 clauses kept 3177
% 1.99/2.21 clauses forward subsumed 16683
% 1.99/2.21 clauses back subsumed 923
% 1.99/2.21 Kbytes malloced 4882
% 1.99/2.21
% 1.99/2.21 ----------- times (seconds) -----------
% 1.99/2.21 user CPU time 0.30 (0 hr, 0 min, 0 sec)
% 1.99/2.21 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.21 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.99/2.21
% 1.99/2.21 That finishes the proof of the theorem.
% 1.99/2.21
% 1.99/2.21 Process 25771 finished Wed Jul 27 02:08:07 2022
% 1.99/2.21 Otter interrupted
% 1.99/2.21 PROOF FOUND
%------------------------------------------------------------------------------