TSTP Solution File: NUM463+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM463+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:08:27 EDT 2022
% Result : Theorem 3.41s 3.58s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of clauses : 27 ( 18 unt; 5 nHn; 27 RR)
% Number of literals : 48 ( 19 equ; 19 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtasdt0(A,B) = sdtasdt0(B,A) ),
file('NUM463+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ aNaturalNumber0(A)
| A = sdtasdt0(sz10,A) ),
file('NUM463+2.p',unknown),
[] ).
cnf(13,plain,
( ~ aNaturalNumber0(A)
| sdtasdt0(sz10,A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.2')] ).
cnf(14,axiom,
( ~ aNaturalNumber0(A)
| sdtasdt0(A,sz00) = sz00 ),
file('NUM463+2.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtlse_qdt0(A,B)
| sdtlse_qdt0(B,A) ),
file('NUM463+2.p',unknown),
[] ).
cnf(42,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(C)
| A = sz00
| B = C
| ~ sdtlse_qdt0(B,C)
| sdtlse_qdt0(sdtasdt0(B,A),sdtasdt0(C,A)) ),
file('NUM463+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ aNaturalNumber0(A)
| A = sz00
| A = sz10
| sz10 != A ),
file('NUM463+2.p',unknown),
[] ).
cnf(44,axiom,
( ~ aNaturalNumber0(A)
| A = sz00
| A = sz10
| sdtlse_qdt0(sz10,A) ),
file('NUM463+2.p',unknown),
[] ).
cnf(45,axiom,
xm != sz00,
file('NUM463+2.p',unknown),
[] ).
cnf(47,axiom,
~ sdtlse_qdt0(xn,sdtasdt0(xn,xm)),
file('NUM463+2.p',unknown),
[] ).
cnf(109,axiom,
aNaturalNumber0(sz00),
file('NUM463+2.p',unknown),
[] ).
cnf(110,axiom,
aNaturalNumber0(sz10),
file('NUM463+2.p',unknown),
[] ).
cnf(111,axiom,
aNaturalNumber0(xm),
file('NUM463+2.p',unknown),
[] ).
cnf(112,axiom,
aNaturalNumber0(xn),
file('NUM463+2.p',unknown),
[] ).
cnf(123,plain,
sdtlse_qdt0(sz00,sz00),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[109,38,109])]),
[iquote('hyper,109,38,109,factor_simp')] ).
cnf(305,plain,
sdtlse_qdt0(xm,xm),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[111,38,111])]),
[iquote('hyper,111,38,111,factor_simp')] ).
cnf(335,plain,
sdtasdt0(xm,sz00) = sz00,
inference(hyper,[status(thm)],[111,14]),
[iquote('hyper,111,14')] ).
cnf(581,plain,
sdtlse_qdt0(xn,xn),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[112,38,112])]),
[iquote('hyper,112,38,112,factor_simp')] ).
cnf(662,plain,
sdtasdt0(sz10,xn) = xn,
inference(hyper,[status(thm)],[112,13]),
[iquote('hyper,112,13')] ).
cnf(686,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[112,9,111])]),
[iquote('hyper,112,9,111,flip.1')] ).
cnf(782,plain,
~ sdtlse_qdt0(xn,sdtasdt0(xm,xn)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),686]),
[iquote('back_demod,47,demod,686')] ).
cnf(1025,plain,
sdtlse_qdt0(sz10,xm),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[305,44]),111,45])]),
[iquote('para_into,305.1.1,44.3.1,unit_del,111,45,factor_simp')] ).
cnf(1166,plain,
( xn = sz00
| xm = sz10 ),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1025,42,112,110,111]),662]),782])]),
[iquote('hyper,1025,42,112,110,111,demod,662,unit_del,782,flip.2')] ).
cnf(5518,plain,
xm != sz10,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[782,43]),662]),581,111,45])]),
[iquote('para_into,782.1.2.1,43.3.1,demod,662,unit_del,581,111,45,flip.1')] ).
cnf(5557,plain,
xn = sz00,
inference(hyper,[status(thm)],[1166,5518]),
[iquote('hyper,1166,5518')] ).
cnf(5559,plain,
~ sdtlse_qdt0(sz00,sz00),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[782]),5557,5557,335]),
[iquote('back_demod,782,demod,5557,5557,335')] ).
cnf(5560,plain,
$false,
inference(binary,[status(thm)],[5559,123]),
[iquote('binary,5559.1,123.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM463+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 09:56:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.91/2.12 ----- Otter 3.3f, August 2004 -----
% 1.91/2.12 The process was started by sandbox2 on n029.cluster.edu,
% 1.91/2.12 Wed Jul 27 09:56:44 2022
% 1.91/2.12 The command was "./otter". The process ID is 28263.
% 1.91/2.12
% 1.91/2.12 set(prolog_style_variables).
% 1.91/2.12 set(auto).
% 1.91/2.12 dependent: set(auto1).
% 1.91/2.12 dependent: set(process_input).
% 1.91/2.12 dependent: clear(print_kept).
% 1.91/2.12 dependent: clear(print_new_demod).
% 1.91/2.12 dependent: clear(print_back_demod).
% 1.91/2.12 dependent: clear(print_back_sub).
% 1.91/2.12 dependent: set(control_memory).
% 1.91/2.12 dependent: assign(max_mem, 12000).
% 1.91/2.12 dependent: assign(pick_given_ratio, 4).
% 1.91/2.12 dependent: assign(stats_level, 1).
% 1.91/2.12 dependent: assign(max_seconds, 10800).
% 1.91/2.12 clear(print_given).
% 1.91/2.12
% 1.91/2.12 formula_list(usable).
% 1.91/2.12 all A (A=A).
% 1.91/2.12 all W0 (aNaturalNumber0(W0)->$T).
% 1.91/2.12 aNaturalNumber0(sz00).
% 1.91/2.12 aNaturalNumber0(sz10).
% 1.91/2.12 sz10!=sz00.
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtpldt0(W0,W1))).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtasdt0(W0,W1))).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtpldt0(W0,W1)=sdtpldt0(W1,W0)).
% 1.91/2.12 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2))).
% 1.91/2.12 all W0 (aNaturalNumber0(W0)->sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtasdt0(W0,W1)=sdtasdt0(W1,W0)).
% 1.91/2.12 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2))).
% 1.91/2.12 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)).
% 1.91/2.12 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)).
% 1.91/2.12 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))&sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))).
% 1.91/2.12 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtpldt0(W0,W1)=sdtpldt0(W0,W2)|sdtpldt0(W1,W0)=sdtpldt0(W2,W0)->W1=W2)).
% 1.91/2.12 all W0 (aNaturalNumber0(W0)-> (W0!=sz00-> (all W1 W2 (aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtasdt0(W0,W1)=sdtasdt0(W0,W2)|sdtasdt0(W1,W0)=sdtasdt0(W2,W0)->W1=W2))))).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtpldt0(W0,W1)=sz00->W0=sz00&W1=sz00)).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtasdt0(W0,W1)=sz00->W0=sz00|W1=sz00)).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)<-> (exists W2 (aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)-> (all W2 (W2=sdtmndt0(W1,W0)<->aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))).
% 1.91/2.12 all W0 (aNaturalNumber0(W0)->sdtlse_qdt0(W0,W0)).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W0)->W0=W1)).
% 1.91/2.12 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W2)->sdtlse_qdt0(W0,W2))).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtlse_qdt0(W0,W1)|W1!=W0&sdtlse_qdt0(W1,W0)).
% 1.91/2.12 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=W1&sdtlse_qdt0(W0,W1)-> (all W2 (aNaturalNumber0(W2)->sdtpldt0(W2,W0)!=sdtpldt0(W2,W1)&sdtlse_qdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))&sdtpldt0(W0,W2)!=sdtpldt0(W1,W2)&sdtlse_qdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)))))).
% 1.91/2.12 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (W0!=sz00&W1!=W2&sdtlse_qdt0(W1,W2)->sdtasdt0(W0,W1)!=sdtasdt0(W0,W2)&sdtlse_qdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))&sdtasdt0(W1,W0)!=sdtasdt0(W2,W0)&sdtlse_qdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)))).
% 1.91/2.12 all W0 (aNaturalNumber0(W0)->W0=sz00|W0=sz10|sz10!=W0&sdtlse_qdt0(sz10,W0)).
% 1.91/2.12 aNaturalNumber0(xm).
% 1.91/2.12 aNaturalNumber0(xn).
% 1.91/2.12 -(xm!=sz00-> (exists W0 (aNaturalNumber0(W0)&sdtpldt0(xn,W0)=sdtasdt0(xn,xm)))|sdtlse_qdt0(xn,sdtasdt0(xn,xm))).
% 1.91/2.12 end_of_list.
% 1.91/2.12
% 1.91/2.12 -------> usable clausifies to:
% 1.91/2.12
% 1.91/2.12 list(usable).
% 1.91/2.12 0 [] A=A.
% 1.91/2.12 0 [] -aNaturalNumber0(W0)|$T.
% 1.91/2.12 0 [] aNaturalNumber0(sz00).
% 1.91/2.12 0 [] aNaturalNumber0(sz10).
% 1.91/2.12 0 [] sz10!=sz00.
% 1.91/2.12 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtpldt0(W0,W1)).
% 1.91/2.12 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtasdt0(W0,W1)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)=sdtpldt0(W1,W0).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|sdtpldt0(W0,sz00)=W0.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|W0=sdtpldt0(sz00,W0).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)=sdtasdt0(W1,W0).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz10)=W0.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|W0=sdtasdt0(sz10,W0).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz00)=sz00.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|sz00=sdtasdt0(sz00,W0).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W1)!=sdtpldt0(W0,W2)|W1=W2.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W1,W0)!=sdtpldt0(W2,W0)|W1=W2.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2)|W1=W2.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0)|W1=W2.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W0=sz00.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W1=sz00.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)!=sz00|W0=sz00|W1=sz00.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|aNaturalNumber0($f1(W0,W1)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|sdtpldt0(W0,$f1(W0,W1))=W1.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=W1.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2!=sdtmndt0(W1,W0)|aNaturalNumber0(W2).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2!=sdtmndt0(W1,W0)|sdtpldt0(W0,W2)=W1.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2=sdtmndt0(W1,W0)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=W1.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|sdtlse_qdt0(W0,W0).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W0)|W0=W1.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(W0,W2).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)|W1!=W0.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)|sdtlse_qdt0(W1,W0).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W2,W0)!=sdtpldt0(W2,W1).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtlse_qdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=sdtpldt0(W1,W2).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtlse_qdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|sz10!=W0.
% 1.91/2.13 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|sdtlse_qdt0(sz10,W0).
% 1.91/2.13 0 [] aNaturalNumber0(xm).
% 1.91/2.13 0 [] aNaturalNumber0(xn).
% 1.91/2.14 0 [] xm!=sz00.
% 1.91/2.14 0 [] -aNaturalNumber0(W0)|sdtpldt0(xn,W0)!=sdtasdt0(xn,xm).
% 1.91/2.14 0 [] -sdtlse_qdt0(xn,sdtasdt0(xn,xm)).
% 1.91/2.14 end_of_list.
% 1.91/2.14
% 1.91/2.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.91/2.14
% 1.91/2.14 This ia a non-Horn set with equality. The strategy will be
% 1.91/2.14 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.91/2.14 deletion, with positive clauses in sos and nonpositive
% 1.91/2.14 clauses in usable.
% 1.91/2.14
% 1.91/2.14 dependent: set(knuth_bendix).
% 1.91/2.14 dependent: set(anl_eq).
% 1.91/2.14 dependent: set(para_from).
% 1.91/2.14 dependent: set(para_into).
% 1.91/2.14 dependent: clear(para_from_right).
% 1.91/2.14 dependent: clear(para_into_right).
% 1.91/2.14 dependent: set(para_from_vars).
% 1.91/2.14 dependent: set(eq_units_both_ways).
% 1.91/2.14 dependent: set(dynamic_demod_all).
% 1.91/2.14 dependent: set(dynamic_demod).
% 1.91/2.14 dependent: set(order_eq).
% 1.91/2.14 dependent: set(back_demod).
% 1.91/2.14 dependent: set(lrpo).
% 1.91/2.14 dependent: set(hyper_res).
% 1.91/2.14 dependent: set(unit_deletion).
% 1.91/2.14 dependent: set(factor).
% 1.91/2.14
% 1.91/2.14 ------------> process usable:
% 1.91/2.14 ** KEPT (pick-wt=3): 1 [] sz10!=sz00.
% 1.91/2.14 ** KEPT (pick-wt=8): 2 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtpldt0(A,B)).
% 1.91/2.14 ** KEPT (pick-wt=8): 3 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtasdt0(A,B)).
% 1.91/2.14 ** KEPT (pick-wt=11): 4 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)=sdtpldt0(B,A).
% 1.91/2.14 ** KEPT (pick-wt=17): 5 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtpldt0(A,B),C)=sdtpldt0(A,sdtpldt0(B,C)).
% 1.91/2.14 ** KEPT (pick-wt=7): 6 [] -aNaturalNumber0(A)|sdtpldt0(A,sz00)=A.
% 1.91/2.14 ** KEPT (pick-wt=7): 8 [copy,7,flip.2] -aNaturalNumber0(A)|sdtpldt0(sz00,A)=A.
% 1.91/2.14 ** KEPT (pick-wt=11): 9 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)=sdtasdt0(B,A).
% 1.91/2.14 ** KEPT (pick-wt=17): 10 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(sdtasdt0(A,B),C)=sdtasdt0(A,sdtasdt0(B,C)).
% 1.91/2.14 ** KEPT (pick-wt=7): 11 [] -aNaturalNumber0(A)|sdtasdt0(A,sz10)=A.
% 1.91/2.14 ** KEPT (pick-wt=7): 13 [copy,12,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz10,A)=A.
% 1.91/2.14 ** KEPT (pick-wt=7): 14 [] -aNaturalNumber0(A)|sdtasdt0(A,sz00)=sz00.
% 1.91/2.14 ** KEPT (pick-wt=7): 16 [copy,15,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz00,A)=sz00.
% 1.91/2.14 ** KEPT (pick-wt=19): 18 [copy,17,flip.4] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))=sdtasdt0(A,sdtpldt0(B,C)).
% 1.91/2.14 ** KEPT (pick-wt=19): 20 [copy,19,flip.4] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A))=sdtasdt0(sdtpldt0(B,C),A).
% 1.91/2.14 ** KEPT (pick-wt=16): 21 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(A,B)!=sdtpldt0(A,C)|B=C.
% 1.91/2.14 ** KEPT (pick-wt=16): 22 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(B,A)!=sdtpldt0(C,A)|B=C.
% 1.91/2.14 ** KEPT (pick-wt=19): 23 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(A,B)!=sdtasdt0(A,C)|B=C.
% 1.91/2.14 ** KEPT (pick-wt=19): 24 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(B,A)!=sdtasdt0(C,A)|B=C.
% 1.91/2.14 ** KEPT (pick-wt=12): 25 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|A=sz00.
% 1.91/2.14 ** KEPT (pick-wt=12): 26 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|B=sz00.
% 1.91/2.14 ** KEPT (pick-wt=15): 27 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)!=sz00|A=sz00|B=sz00.
% 1.91/2.14 ** KEPT (pick-wt=11): 28 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|aNaturalNumber0($f1(A,B)).
% 1.91/2.14 ** KEPT (pick-wt=14): 29 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|sdtpldt0(A,$f1(A,B))=B.
% 1.91/2.14 ** KEPT (pick-wt=14): 30 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=B.
% 1.91/2.14 ** KEPT (pick-wt=14): 31 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C!=sdtmndt0(B,A)|aNaturalNumber0(C).
% 1.91/2.14 ** KEPT (pick-wt=17): 32 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C!=sdtmndt0(B,A)|sdtpldt0(A,C)=B.
% 1.91/2.14 ** KEPT (pick-wt=19): 33 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C=sdtmndt0(B,A)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=B.
% 1.91/2.14 ** KEPT (pick-wt=5): 34 [] -aNaturalNumber0(A)|sdtlse_qdt0(A,A).
% 1.91/2.14 ** KEPT (pick-wt=13): 35 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,A)|A=B.
% 3.41/3.58 ** KEPT (pick-wt=15): 36 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,C)|sdtlse_qdt0(A,C).
% 3.41/3.58 ** KEPT (pick-wt=10): 37 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)|B!=A.
% 3.41/3.58 ** KEPT (pick-wt=10): 38 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)|sdtlse_qdt0(B,A).
% 3.41/3.58 Following clause subsumed by 21 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(C,A)!=sdtpldt0(C,B).
% 3.41/3.58 ** KEPT (pick-wt=19): 39 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtlse_qdt0(sdtpldt0(C,A),sdtpldt0(C,B)).
% 3.41/3.58 Following clause subsumed by 22 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=sdtpldt0(B,C).
% 3.41/3.58 ** KEPT (pick-wt=19): 40 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtlse_qdt0(sdtpldt0(A,C),sdtpldt0(B,C)).
% 3.41/3.58 Following clause subsumed by 23 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtasdt0(A,B)!=sdtasdt0(A,C).
% 3.41/3.58 ** KEPT (pick-wt=22): 41 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtlse_qdt0(sdtasdt0(A,B),sdtasdt0(A,C)).
% 3.41/3.58 Following clause subsumed by 24 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtasdt0(B,A)!=sdtasdt0(C,A).
% 3.41/3.58 ** KEPT (pick-wt=22): 42 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtlse_qdt0(sdtasdt0(B,A),sdtasdt0(C,A)).
% 3.41/3.58 ** KEPT (pick-wt=11): 43 [] -aNaturalNumber0(A)|A=sz00|A=sz10|sz10!=A.
% 3.41/3.58 ** KEPT (pick-wt=11): 44 [] -aNaturalNumber0(A)|A=sz00|A=sz10|sdtlse_qdt0(sz10,A).
% 3.41/3.58 ** KEPT (pick-wt=3): 45 [] xm!=sz00.
% 3.41/3.58 ** KEPT (pick-wt=9): 46 [] -aNaturalNumber0(A)|sdtpldt0(xn,A)!=sdtasdt0(xn,xm).
% 3.41/3.58 ** KEPT (pick-wt=5): 47 [] -sdtlse_qdt0(xn,sdtasdt0(xn,xm)).
% 3.41/3.58
% 3.41/3.58 ------------> process sos:
% 3.41/3.58 ** KEPT (pick-wt=3): 108 [] A=A.
% 3.41/3.58 ** KEPT (pick-wt=2): 109 [] aNaturalNumber0(sz00).
% 3.41/3.58 ** KEPT (pick-wt=2): 110 [] aNaturalNumber0(sz10).
% 3.41/3.58 ** KEPT (pick-wt=2): 111 [] aNaturalNumber0(xm).
% 3.41/3.58 ** KEPT (pick-wt=2): 112 [] aNaturalNumber0(xn).
% 3.41/3.58 Following clause subsumed by 108 during input processing: 0 [copy,108,flip.1] A=A.
% 3.41/3.58 108 back subsumes 106.
% 3.41/3.58 108 back subsumes 105.
% 3.41/3.58 108 back subsumes 104.
% 3.41/3.58 108 back subsumes 89.
% 3.41/3.58 108 back subsumes 77.
% 3.41/3.58 108 back subsumes 73.
% 3.41/3.58 108 back subsumes 69.
% 3.41/3.58 108 back subsumes 66.
% 3.41/3.58 108 back subsumes 54.
% 3.41/3.58 108 back subsumes 50.
% 3.41/3.58
% 3.41/3.58 ======= end of input processing =======
% 3.41/3.58
% 3.41/3.58 =========== start of search ===========
% 3.41/3.58
% 3.41/3.58
% 3.41/3.58 Resetting weight limit to 8.
% 3.41/3.58
% 3.41/3.58
% 3.41/3.58 Resetting weight limit to 8.
% 3.41/3.58
% 3.41/3.58 sos_size=1851
% 3.41/3.58
% 3.41/3.58
% 3.41/3.58 Resetting weight limit to 6.
% 3.41/3.58
% 3.41/3.58
% 3.41/3.58 Resetting weight limit to 6.
% 3.41/3.58
% 3.41/3.58 sos_size=2331
% 3.41/3.58
% 3.41/3.58 -------- PROOF --------
% 3.41/3.58
% 3.41/3.58 ----> UNIT CONFLICT at 1.46 sec ----> 5560 [binary,5559.1,123.1] $F.
% 3.41/3.58
% 3.41/3.58 Length of proof is 13. Level of proof is 5.
% 3.41/3.58
% 3.41/3.58 ---------------- PROOF ----------------
% 3.41/3.58 % SZS status Theorem
% 3.41/3.58 % SZS output start Refutation
% See solution above
% 3.41/3.58 ------------ end of proof -------------
% 3.41/3.58
% 3.41/3.58
% 3.41/3.58 Search stopped by max_proofs option.
% 3.41/3.58
% 3.41/3.58
% 3.41/3.58 Search stopped by max_proofs option.
% 3.41/3.58
% 3.41/3.58 ============ end of search ============
% 3.41/3.58
% 3.41/3.58 -------------- statistics -------------
% 3.41/3.58 clauses given 102
% 3.41/3.58 clauses generated 99006
% 3.41/3.58 clauses kept 3517
% 3.41/3.58 clauses forward subsumed 9946
% 3.41/3.58 clauses back subsumed 111
% 3.41/3.58 Kbytes malloced 5859
% 3.41/3.58
% 3.41/3.58 ----------- times (seconds) -----------
% 3.41/3.58 user CPU time 1.46 (0 hr, 0 min, 1 sec)
% 3.41/3.58 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.41/3.58 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.41/3.58
% 3.41/3.58 That finishes the proof of the theorem.
% 3.41/3.58
% 3.41/3.58 Process 28263 finished Wed Jul 27 09:56:47 2022
% 3.41/3.58 Otter interrupted
% 3.41/3.58 PROOF FOUND
%------------------------------------------------------------------------------