TSTP Solution File: RNG006-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG006-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 2.14s 2.32s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 10 RR)
% Number of literals : 15 ( 0 equ; 6 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ sum(C,E,G)
| product(A,F,G) ),
file('RNG006-2.p',unknown),
[] ).
cnf(21,axiom,
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ),
file('RNG006-2.p',unknown),
[] ).
cnf(24,axiom,
~ product(a,bS_Ic,aPb_S_IaPc),
file('RNG006-2.p',unknown),
[] ).
cnf(33,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('RNG006-2.p',unknown),
[] ).
cnf(34,axiom,
product(a,b,aPb),
file('RNG006-2.p',unknown),
[] ).
cnf(35,axiom,
product(a,c,aPc),
file('RNG006-2.p',unknown),
[] ).
cnf(36,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('RNG006-2.p',unknown),
[] ).
cnf(123,plain,
product(a,additive_inverse(c),additive_inverse(aPc)),
inference(hyper,[status(thm)],[35,21]),
[iquote('hyper,35,21')] ).
cnf(6052,plain,
product(a,bS_Ic,aPb_S_IaPc),
inference(hyper,[status(thm)],[123,16,34,33,36]),
[iquote('hyper,123,16,34,33,36')] ).
cnf(6053,plain,
$false,
inference(binary,[status(thm)],[6052,24]),
[iquote('binary,6052.1,24.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n014.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 02:17:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.79/1.97 ----- Otter 3.3f, August 2004 -----
% 1.79/1.97 The process was started by sandbox on n014.cluster.edu,
% 1.79/1.97 Wed Jul 27 02:17:54 2022
% 1.79/1.97 The command was "./otter". The process ID is 17980.
% 1.79/1.97
% 1.79/1.97 set(prolog_style_variables).
% 1.79/1.97 set(auto).
% 1.79/1.97 dependent: set(auto1).
% 1.79/1.97 dependent: set(process_input).
% 1.79/1.97 dependent: clear(print_kept).
% 1.79/1.97 dependent: clear(print_new_demod).
% 1.79/1.97 dependent: clear(print_back_demod).
% 1.79/1.97 dependent: clear(print_back_sub).
% 1.79/1.97 dependent: set(control_memory).
% 1.79/1.97 dependent: assign(max_mem, 12000).
% 1.79/1.97 dependent: assign(pick_given_ratio, 4).
% 1.79/1.97 dependent: assign(stats_level, 1).
% 1.79/1.97 dependent: assign(max_seconds, 10800).
% 1.79/1.97 clear(print_given).
% 1.79/1.97
% 1.79/1.97 list(usable).
% 1.79/1.97 0 [] -e_qualish(X,Y)|e_qualish(additive_inverse(X),additive_inverse(Y)).
% 1.79/1.97 0 [] -e_qualish(X,Y)|e_qualish(add(X,W),add(Y,W)).
% 1.79/1.97 0 [] -e_qualish(X,Y)| -sum(X,W,Z)|sum(Y,W,Z).
% 1.79/1.97 0 [] -e_qualish(X,Y)| -sum(W,X,Z)|sum(W,Y,Z).
% 1.79/1.97 0 [] -e_qualish(X,Y)| -sum(W,Z,X)|sum(W,Z,Y).
% 1.79/1.97 0 [] -e_qualish(X,Y)|e_qualish(multiply(X,W),multiply(Y,W)).
% 1.79/1.97 0 [] -e_qualish(X,Y)| -product(X,W,Z)|product(Y,W,Z).
% 1.79/1.97 0 [] -e_qualish(X,Y)| -product(W,X,Z)|product(W,Y,Z).
% 1.79/1.97 0 [] -e_qualish(X,Y)| -product(W,Z,X)|product(W,Z,Y).
% 1.79/1.97 0 [] sum(additive_identity,X,X).
% 1.79/1.97 0 [] sum(X,additive_identity,X).
% 1.79/1.97 0 [] product(X,Y,multiply(X,Y)).
% 1.79/1.97 0 [] sum(X,Y,add(X,Y)).
% 1.79/1.97 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.79/1.97 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.79/1.97 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.79/1.97 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.79/1.97 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.79/1.97 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.79/1.97 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.79/1.97 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.79/1.97 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.79/1.97 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.79/1.97 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.79/1.97 0 [] -sum(X,Y,U)| -sum(X,Y,V)|e_qualish(U,V).
% 1.79/1.97 0 [] -product(X,Y,U)| -product(X,Y,V)|e_qualish(U,V).
% 1.79/1.97 0 [] product(additive_identity,X,additive_identity).
% 1.79/1.97 0 [] product(X,additive_identity,additive_identity).
% 1.79/1.97 0 [] -product(A,B,C)|product(A,additive_inverse(B),additive_inverse(C)).
% 1.79/1.97 0 [] -product(A,B,C)|product(additive_inverse(A),B,additive_inverse(C)).
% 1.79/1.97 0 [] -product(A,B,C)|product(additive_inverse(A),additive_inverse(B),C).
% 1.79/1.97 0 [] sum(b,additive_inverse(c),bS_Ic).
% 1.79/1.97 0 [] product(a,b,aPb).
% 1.79/1.97 0 [] product(a,c,aPc).
% 1.79/1.97 0 [] sum(aPb,additive_inverse(aPc),aPb_S_IaPc).
% 1.79/1.97 0 [] -product(a,bS_Ic,aPb_S_IaPc).
% 1.79/1.97 end_of_list.
% 1.79/1.97
% 1.79/1.97 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=5.
% 1.79/1.97
% 1.79/1.97 This is a Horn set without equality. The strategy will
% 1.79/1.97 be hyperresolution, with satellites in sos and nuclei
% 1.79/1.97 in usable.
% 1.79/1.97
% 1.79/1.97 dependent: set(hyper_res).
% 1.79/1.97 dependent: clear(order_hyper).
% 1.79/1.97
% 1.79/1.97 ------------> process usable:
% 1.79/1.97 ** KEPT (pick-wt=8): 1 [] -e_qualish(A,B)|e_qualish(additive_inverse(A),additive_inverse(B)).
% 1.79/1.97 ** KEPT (pick-wt=10): 2 [] -e_qualish(A,B)|e_qualish(add(A,C),add(B,C)).
% 1.79/1.97 ** KEPT (pick-wt=11): 3 [] -e_qualish(A,B)| -sum(A,C,D)|sum(B,C,D).
% 1.79/1.97 ** KEPT (pick-wt=11): 4 [] -e_qualish(A,B)| -sum(C,A,D)|sum(C,B,D).
% 1.79/1.97 ** KEPT (pick-wt=11): 5 [] -e_qualish(A,B)| -sum(C,D,A)|sum(C,D,B).
% 1.79/1.97 ** KEPT (pick-wt=10): 6 [] -e_qualish(A,B)|e_qualish(multiply(A,C),multiply(B,C)).
% 1.79/1.97 ** KEPT (pick-wt=11): 7 [] -e_qualish(A,B)| -product(A,C,D)|product(B,C,D).
% 1.79/1.97 ** KEPT (pick-wt=11): 8 [] -e_qualish(A,B)| -product(C,A,D)|product(C,B,D).
% 1.79/1.97 ** KEPT (pick-wt=11): 9 [] -e_qualish(A,B)| -product(C,D,A)|product(C,D,B).
% 1.79/1.97 ** KEPT (pick-wt=16): 10 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.79/1.97 ** KEPT (pick-wt=16): 11 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.79/1.97 ** KEPT (pick-wt=8): 12 [] -sum(A,B,C)|sum(B,A,C).
% 1.79/1.97 ** KEPT (pick-wt=16): 13 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.79/1.97 ** KEPT (pick-wt=16): 14 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.79/1.97 ** KEPT (pick-wt=20): 15 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 1.79/1.97 ** KEPT (pick-wt=20): 16 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 2.14/2.32 ** KEPT (pick-wt=20): 17 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 2.14/2.32 ** KEPT (pick-wt=20): 18 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 2.14/2.32 ** KEPT (pick-wt=11): 19 [] -sum(A,B,C)| -sum(A,B,D)|e_qualish(C,D).
% 2.14/2.32 ** KEPT (pick-wt=11): 20 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 2.14/2.32 ** KEPT (pick-wt=10): 21 [] -product(A,B,C)|product(A,additive_inverse(B),additive_inverse(C)).
% 2.14/2.32 ** KEPT (pick-wt=10): 22 [] -product(A,B,C)|product(additive_inverse(A),B,additive_inverse(C)).
% 2.14/2.32 ** KEPT (pick-wt=10): 23 [] -product(A,B,C)|product(additive_inverse(A),additive_inverse(B),C).
% 2.14/2.32 ** KEPT (pick-wt=4): 24 [] -product(a,bS_Ic,aPb_S_IaPc).
% 2.14/2.32
% 2.14/2.32 ------------> process sos:
% 2.14/2.32 ** KEPT (pick-wt=4): 25 [] sum(additive_identity,A,A).
% 2.14/2.32 ** KEPT (pick-wt=4): 26 [] sum(A,additive_identity,A).
% 2.14/2.32 ** KEPT (pick-wt=6): 27 [] product(A,B,multiply(A,B)).
% 2.14/2.32 ** KEPT (pick-wt=6): 28 [] sum(A,B,add(A,B)).
% 2.14/2.32 ** KEPT (pick-wt=5): 29 [] sum(additive_inverse(A),A,additive_identity).
% 2.14/2.32 ** KEPT (pick-wt=5): 30 [] sum(A,additive_inverse(A),additive_identity).
% 2.14/2.32 ** KEPT (pick-wt=4): 31 [] product(additive_identity,A,additive_identity).
% 2.14/2.32 ** KEPT (pick-wt=4): 32 [] product(A,additive_identity,additive_identity).
% 2.14/2.32 ** KEPT (pick-wt=5): 33 [] sum(b,additive_inverse(c),bS_Ic).
% 2.14/2.32 ** KEPT (pick-wt=4): 34 [] product(a,b,aPb).
% 2.14/2.32 ** KEPT (pick-wt=4): 35 [] product(a,c,aPc).
% 2.14/2.32 ** KEPT (pick-wt=5): 36 [] sum(aPb,additive_inverse(aPc),aPb_S_IaPc).
% 2.14/2.32
% 2.14/2.32 ======= end of input processing =======
% 2.14/2.32
% 2.14/2.32 =========== start of search ===========
% 2.14/2.32
% 2.14/2.32
% 2.14/2.32 Resetting weight limit to 7.
% 2.14/2.32
% 2.14/2.32
% 2.14/2.32 Resetting weight limit to 7.
% 2.14/2.32
% 2.14/2.32 sos_size=5095
% 2.14/2.32
% 2.14/2.32 -------- PROOF --------
% 2.14/2.32
% 2.14/2.32 ----> UNIT CONFLICT at 0.34 sec ----> 6053 [binary,6052.1,24.1] $F.
% 2.14/2.32
% 2.14/2.32 Length of proof is 2. Level of proof is 2.
% 2.14/2.32
% 2.14/2.32 ---------------- PROOF ----------------
% 2.14/2.32 % SZS status Unsatisfiable
% 2.14/2.32 % SZS output start Refutation
% See solution above
% 2.14/2.32 ------------ end of proof -------------
% 2.14/2.32
% 2.14/2.32
% 2.14/2.32 Search stopped by max_proofs option.
% 2.14/2.32
% 2.14/2.32
% 2.14/2.32 Search stopped by max_proofs option.
% 2.14/2.32
% 2.14/2.32 ============ end of search ============
% 2.14/2.32
% 2.14/2.32 -------------- statistics -------------
% 2.14/2.32 clauses given 82
% 2.14/2.32 clauses generated 104214
% 2.14/2.32 clauses kept 6052
% 2.14/2.32 clauses forward subsumed 37791
% 2.14/2.32 clauses back subsumed 777
% 2.14/2.32 Kbytes malloced 4882
% 2.14/2.32
% 2.14/2.32 ----------- times (seconds) -----------
% 2.14/2.32 user CPU time 0.34 (0 hr, 0 min, 0 sec)
% 2.14/2.32 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.14/2.32 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.14/2.32
% 2.14/2.32 That finishes the proof of the theorem.
% 2.14/2.32
% 2.14/2.32 Process 17980 finished Wed Jul 27 02:17:56 2022
% 2.14/2.32 Otter interrupted
% 2.14/2.32 PROOF FOUND
%------------------------------------------------------------------------------