TSTP Solution File: RNG010-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 : Tue Apr 30 14:50:16 EDT 2024
% Result : Unsatisfiable 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 34
% Syntax : Number of formulae : 68 ( 31 unt; 0 def)
% Number of atoms : 115 ( 49 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 83 ( 36 ~; 29 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f284,plain,
$false,
inference(avatar_sat_refutation,[],[f32,f36,f40,f44,f48,f53,f59,f63,f75,f79,f107,f111,f115,f133,f159,f163,f167,f171,f266,f268]) ).
fof(f268,plain,
( ~ spl0_15
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f267,plain,
( $false
| ~ spl0_15
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f261]) ).
fof(f261,plain,
( ! [X0] : multiply(X0,multiply(X0,X0)) != multiply(X0,multiply(X0,X0))
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f170,f158]) ).
fof(f158,plain,
( ! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f157,plain,
( spl0_15
<=> ! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f170,plain,
( ! [X0,X1] : multiply(multiply(X1,X0),X1) != multiply(X1,multiply(X0,X1))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f169,plain,
( spl0_18
<=> ! [X0,X1] : multiply(multiply(X1,X0),X1) != multiply(X1,multiply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f266,plain,
( ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f265,plain,
( $false
| ~ spl0_16
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f262]) ).
fof(f262,plain,
( ! [X0] : multiply(X0,multiply(X0,X0)) != multiply(X0,multiply(X0,X0))
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f170,f162]) ).
fof(f162,plain,
( ! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f161,plain,
( spl0_16
<=> ! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f171,plain,
spl0_18,
inference(avatar_split_clause,[],[f19,f169]) ).
fof(f19,axiom,
! [X0,X1] : multiply(multiply(X1,X0),X1) != multiply(X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',middle_law) ).
fof(f167,plain,
spl0_17,
inference(avatar_split_clause,[],[f15,f165]) ).
fof(f165,plain,
( spl0_17
<=> ! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f163,plain,
spl0_16,
inference(avatar_split_clause,[],[f10,f161]) ).
fof(f10,axiom,
! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_alternative) ).
fof(f159,plain,
spl0_15,
inference(avatar_split_clause,[],[f9,f157]) ).
fof(f9,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_alternative) ).
fof(f133,plain,
( spl0_14
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f64,f61,f34,f131]) ).
fof(f131,plain,
( spl0_14
<=> ! [X0] : add(X0,additive_identity) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f34,plain,
( spl0_2
<=> ! [X0] : add(additive_identity,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f61,plain,
( spl0_8
<=> ! [X0,X1] : add(X0,X1) = add(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f64,plain,
( ! [X0] : add(X0,additive_identity) = X0
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f62,f35]) ).
fof(f35,plain,
( ! [X0] : add(additive_identity,X0) = X0
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f62,plain,
( ! [X0,X1] : add(X0,X1) = add(X1,X0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f115,plain,
spl0_13,
inference(avatar_split_clause,[],[f17,f113]) ).
fof(f113,plain,
( spl0_13
<=> ! [X2,X0,X1] :
( X0 = X1
| add(X2,X0) != add(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f17,axiom,
! [X2,X0,X1] :
( X0 = X1
| add(X2,X0) != add(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_cancellation_for_addition) ).
fof(f111,plain,
spl0_12,
inference(avatar_split_clause,[],[f16,f109]) ).
fof(f109,plain,
( spl0_12
<=> ! [X2,X0,X1] :
( X0 = X1
| add(X1,X2) != add(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( X0 = X1
| add(X1,X2) != add(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation_for_addition) ).
fof(f107,plain,
spl0_11,
inference(avatar_split_clause,[],[f5,f105]) ).
fof(f105,plain,
( spl0_11
<=> ! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f5,axiom,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_of_inverses) ).
fof(f79,plain,
spl0_10,
inference(avatar_split_clause,[],[f12,f77]) ).
fof(f77,plain,
( spl0_10
<=> ! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f12,axiom,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
fof(f75,plain,
spl0_9,
inference(avatar_split_clause,[],[f11,f73]) ).
fof(f73,plain,
( spl0_9
<=> ! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f11,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
fof(f63,plain,
spl0_8,
inference(avatar_split_clause,[],[f14,f61]) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f59,plain,
( spl0_7
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f55,f51,f46,f57]) ).
fof(f57,plain,
( spl0_7
<=> ! [X0] : additive_identity = add(X0,additive_inverse(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f46,plain,
( spl0_5
<=> ! [X0] : additive_inverse(additive_inverse(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f51,plain,
( spl0_6
<=> ! [X0] : additive_identity = add(additive_inverse(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f55,plain,
( ! [X0] : additive_identity = add(X0,additive_inverse(X0))
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f52,f47]) ).
fof(f47,plain,
( ! [X0] : additive_inverse(additive_inverse(X0)) = X0
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f52,plain,
( ! [X0] : additive_identity = add(additive_inverse(X0),X0)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
spl0_6,
inference(avatar_split_clause,[],[f4,f51]) ).
fof(f4,axiom,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_inverse) ).
fof(f48,plain,
spl0_5,
inference(avatar_split_clause,[],[f6,f46]) ).
fof(f6,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f44,plain,
spl0_4,
inference(avatar_split_clause,[],[f3,f42]) ).
fof(f42,plain,
( spl0_4
<=> ! [X0] : additive_identity = multiply(X0,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f3,axiom,
! [X0] : additive_identity = multiply(X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f40,plain,
spl0_3,
inference(avatar_split_clause,[],[f2,f38]) ).
fof(f38,plain,
( spl0_3
<=> ! [X0] : additive_identity = multiply(additive_identity,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f2,axiom,
! [X0] : additive_identity = multiply(additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_zero) ).
fof(f36,plain,
spl0_2,
inference(avatar_split_clause,[],[f1,f34]) ).
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f32,plain,
spl0_1,
inference(avatar_split_clause,[],[f13,f29]) ).
fof(f29,plain,
( spl0_1
<=> additive_identity = additive_inverse(additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f13,axiom,
additive_identity = additive_inverse(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_additive_identity) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 02:11:46 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (8679)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (8681)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (8682)WARNING: value z3 for option sas not known
% 0.14/0.38 % (8680)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (8683)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (8685)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (8682)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (8684)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (8686)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 % (8684)First to succeed.
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 % (8684)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (8684)------------------------------
% 0.14/0.39 % (8684)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39 % (8684)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (8684)Memory used [KB]: 904
% 0.14/0.39 % (8684)Time elapsed: 0.010 s
% 0.14/0.39 % (8684)Instructions burned: 12 (million)
% 0.14/0.39 % (8684)------------------------------
% 0.14/0.39 % (8684)------------------------------
% 0.14/0.39 % (8679)Success in time 0.026 s
%------------------------------------------------------------------------------