TSTP Solution File: ALG036+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ALG036+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n009.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 Aug 31 15:42:15 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 6 unt; 3 typ; 0 def)
% Number of atoms : 307 ( 210 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 357 ( 116 ~; 143 |; 97 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 4 ( 0 usr; 3 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 2 ( 2 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_5,type,
sQ4_eqProxy: ( $int * $int ) > $o ).
tff(pred_def_6,type,
sQ5_eqProxy: ( $rat * $rat ) > $o ).
tff(pred_def_7,type,
sQ6_eqProxy: ( $real * $real ) > $o ).
fof(f526,plain,
$false,
inference(sat_instgen_refutation,[],[f397,f447,f403,f423,f430,f495,f462,f445,f477,f475,f499,f453,f481,f441,f470,f405,f412,f387,f450,f504]) ).
fof(f504,plain,
( ~ sQ3_eqProxy(op(e2,e2),unit)
| ~ sQ3_eqProxy(op(e3,e3),unit)
| ~ sQ3_eqProxy(unit,op(unit,unit))
| ~ sQ3_eqProxy(op(e1,e1),unit) ),
inference(equality_proxy_replacement,[],[f243,f375,f375,f375,f375]) ).
fof(f375,plain,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ3_eqProxy])]) ).
fof(f243,plain,
( op(e1,e1) != unit
| op(e2,e2) != unit
| unit != op(unit,unit)
| op(e3,e3) != unit ),
inference(definition_unfolding,[],[f140,f148,f148,f148,f148,f148,f148]) ).
fof(f148,plain,
e0 = unit,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
e0 = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f140,plain,
( e0 != op(e1,e1)
| e0 != op(e0,e0)
| e0 != op(e2,e2)
| e0 != op(e3,e3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
( ( op(e0,e0) != e3
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| e3 != op(e3,e3) )
& ( ( e3 = op(e2,e2)
& e3 = op(e1,e1)
& op(e0,e0) = e3
& e3 = op(e3,e3) )
| sP2
| sP1
| sP0 )
& ( e1 != op(e2,e2)
| op(e0,e0) != e1
| e1 != op(e3,e3)
| e1 != op(e1,e1) )
& ( e2 != op(e2,e2)
| op(e0,e0) != e2
| e2 != op(e1,e1)
| e2 != op(e3,e3) )
& ( e0 != op(e1,e1)
| e0 != op(e0,e0)
| e0 != op(e2,e2)
| e0 != op(e3,e3) ) ),
inference(definition_folding,[],[f9,f12,f11,f10]) ).
fof(f10,plain,
( ( e1 = op(e1,e1)
& op(e0,e0) = e1
& e1 = op(e2,e2)
& e1 = op(e3,e3) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f11,plain,
( ( e0 = op(e3,e3)
& e0 = op(e2,e2)
& e0 = op(e0,e0)
& e0 = op(e1,e1) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f12,plain,
( ( op(e0,e0) = e2
& e2 = op(e1,e1)
& e2 = op(e3,e3)
& e2 = op(e2,e2) )
| ~ sP2 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f9,plain,
( ( op(e0,e0) != e3
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| e3 != op(e3,e3) )
& ( ( e3 = op(e2,e2)
& e3 = op(e1,e1)
& op(e0,e0) = e3
& e3 = op(e3,e3) )
| ( op(e0,e0) = e2
& e2 = op(e1,e1)
& e2 = op(e3,e3)
& e2 = op(e2,e2) )
| ( e0 = op(e3,e3)
& e0 = op(e2,e2)
& e0 = op(e0,e0)
& e0 = op(e1,e1) )
| ( e1 = op(e1,e1)
& op(e0,e0) = e1
& e1 = op(e2,e2)
& e1 = op(e3,e3) ) )
& ( e1 != op(e2,e2)
| op(e0,e0) != e1
| e1 != op(e3,e3)
| e1 != op(e1,e1) )
& ( e2 != op(e2,e2)
| op(e0,e0) != e2
| e2 != op(e1,e1)
| e2 != op(e3,e3) )
& ( e0 != op(e1,e1)
| e0 != op(e0,e0)
| e0 != op(e2,e2)
| e0 != op(e3,e3) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ( ~ ( ( e3 = op(e2,e2)
& e3 = op(e1,e1)
& op(e0,e0) = e3
& e3 = op(e3,e3) )
| ( op(e0,e0) = e2
& e2 = op(e1,e1)
& e2 = op(e3,e3)
& e2 = op(e2,e2) )
| ( e0 = op(e3,e3)
& e0 = op(e2,e2)
& e0 = op(e0,e0)
& e0 = op(e1,e1) )
| ( e1 = op(e1,e1)
& op(e0,e0) = e1
& e1 = op(e2,e2)
& e1 = op(e3,e3) ) )
| ( e0 = op(e0,e0)
& e0 = op(e2,e2)
& e0 = op(e3,e3)
& e0 = op(e1,e1) )
| ( op(e0,e0) = e1
& e1 = op(e3,e3)
& e1 = op(e2,e2)
& e1 = op(e1,e1) )
| ( e3 = op(e1,e1)
& e3 = op(e2,e2)
& e3 = op(e3,e3)
& op(e0,e0) = e3 )
| ( e2 = op(e2,e2)
& op(e0,e0) = e2
& e2 = op(e1,e1)
& e2 = op(e3,e3) ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
( ~ ( ( e3 = op(e2,e2)
& e3 = op(e1,e1)
& op(e0,e0) = e3
& e3 = op(e3,e3) )
| ( op(e0,e0) = e2
& e2 = op(e1,e1)
& e2 = op(e3,e3)
& e2 = op(e2,e2) )
| ( e0 = op(e3,e3)
& e0 = op(e2,e2)
& e0 = op(e0,e0)
& e0 = op(e1,e1) )
| ( e1 = op(e1,e1)
& op(e0,e0) = e1
& e1 = op(e2,e2)
& e1 = op(e3,e3) ) )
| ( e0 = op(e0,e0)
& e0 = op(e2,e2)
& e0 = op(e3,e3)
& e0 = op(e1,e1) )
| ( op(e0,e0) = e1
& e1 = op(e3,e3)
& e1 = op(e2,e2)
& e1 = op(e1,e1) )
| ( e3 = op(e1,e1)
& e3 = op(e2,e2)
& e3 = op(e3,e3)
& op(e0,e0) = e3 )
| ( e2 = op(e2,e2)
& op(e0,e0) = e2
& e2 = op(e1,e1)
& e2 = op(e3,e3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f450,plain,
( sQ3_eqProxy(op(e3,e3),unit)
| ~ sP1 ),
inference(equality_proxy_replacement,[],[f234,f375]) ).
fof(f234,plain,
( op(e3,e3) = unit
| ~ sP1 ),
inference(definition_unfolding,[],[f135,f148]) ).
fof(f135,plain,
( e0 = op(e3,e3)
| ~ sP1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( ( e0 = op(e3,e3)
& e0 = op(e2,e2)
& e0 = op(e0,e0)
& e0 = op(e1,e1) )
| ~ sP1 ),
inference(nnf_transformation,[],[f11]) ).
fof(f387,plain,
( ~ sP0
| sQ3_eqProxy(e1,op(e2,e2)) ),
inference(equality_proxy_replacement,[],[f137,f375]) ).
fof(f137,plain,
( e1 = op(e2,e2)
| ~ sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ( e1 = op(e1,e1)
& op(e0,e0) = e1
& e1 = op(e2,e2)
& e1 = op(e3,e3) )
| ~ sP0 ),
inference(nnf_transformation,[],[f10]) ).
fof(f412,plain,
( sP0
| sP2
| sP1
| sQ3_eqProxy(e3,op(e1,e1)) ),
inference(equality_proxy_replacement,[],[f145,f375]) ).
fof(f145,plain,
( sP2
| sP1
| e3 = op(e1,e1)
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f405,plain,
( ~ sQ3_eqProxy(e3,op(unit,unit))
| ~ sQ3_eqProxy(e3,op(e2,e2))
| ~ sQ3_eqProxy(e3,op(e1,e1))
| ~ sQ3_eqProxy(e3,op(e3,e3)) ),
inference(equality_proxy_replacement,[],[f239,f375,f375,f375,f375]) ).
fof(f239,plain,
( e3 != op(unit,unit)
| e3 != op(e3,e3)
| e3 != op(e1,e1)
| e3 != op(e2,e2) ),
inference(definition_unfolding,[],[f147,f148,f148]) ).
fof(f147,plain,
( op(e0,e0) != e3
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| e3 != op(e3,e3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f470,plain,
( ~ sP2
| sQ3_eqProxy(e2,op(e2,e2)) ),
inference(equality_proxy_replacement,[],[f128,f375]) ).
fof(f128,plain,
( e2 = op(e2,e2)
| ~ sP2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
( ( op(e0,e0) = e2
& e2 = op(e1,e1)
& e2 = op(e3,e3)
& e2 = op(e2,e2) )
| ~ sP2 ),
inference(nnf_transformation,[],[f12]) ).
fof(f441,plain,
( ~ sQ3_eqProxy(e1,op(e3,e3))
| ~ sQ3_eqProxy(e1,op(unit,unit))
| ~ sQ3_eqProxy(e1,op(e2,e2))
| ~ sQ3_eqProxy(e1,op(e1,e1)) ),
inference(equality_proxy_replacement,[],[f241,f375,f375,f375,f375]) ).
fof(f241,plain,
( e1 != op(unit,unit)
| e1 != op(e3,e3)
| e1 != op(e1,e1)
| e1 != op(e2,e2) ),
inference(definition_unfolding,[],[f142,f148,f148]) ).
fof(f142,plain,
( e1 != op(e2,e2)
| op(e0,e0) != e1
| e1 != op(e3,e3)
| e1 != op(e1,e1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f481,plain,
( sQ3_eqProxy(op(e1,e1),unit)
| ~ sP1 ),
inference(equality_proxy_replacement,[],[f237,f375]) ).
fof(f237,plain,
( ~ sP1
| op(e1,e1) = unit ),
inference(definition_unfolding,[],[f132,f148]) ).
fof(f132,plain,
( e0 = op(e1,e1)
| ~ sP1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f453,plain,
( ~ sQ3_eqProxy(e2,op(e1,e1))
| ~ sQ3_eqProxy(e2,op(unit,unit))
| ~ sQ3_eqProxy(e2,op(e2,e2))
| ~ sQ3_eqProxy(e2,op(e3,e3)) ),
inference(equality_proxy_replacement,[],[f242,f375,f375,f375,f375]) ).
fof(f242,plain,
( e2 != op(e1,e1)
| e2 != op(unit,unit)
| e2 != op(e2,e2)
| e2 != op(e3,e3) ),
inference(definition_unfolding,[],[f141,f148,f148]) ).
fof(f141,plain,
( e2 != op(e2,e2)
| op(e0,e0) != e2
| e2 != op(e1,e1)
| e2 != op(e3,e3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f499,plain,
( sP2
| sP1
| sP0
| sQ3_eqProxy(e3,op(unit,unit)) ),
inference(equality_proxy_replacement,[],[f240,f375]) ).
fof(f240,plain,
( sP0
| e3 = op(unit,unit)
| sP2
| sP1 ),
inference(definition_unfolding,[],[f144,f148,f148]) ).
fof(f144,plain,
( op(e0,e0) = e3
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f475,plain,
( ~ sP0
| sQ3_eqProxy(e1,op(e1,e1)) ),
inference(equality_proxy_replacement,[],[f139,f375]) ).
fof(f139,plain,
( ~ sP0
| e1 = op(e1,e1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f477,plain,
( ~ sP2
| sQ3_eqProxy(e2,op(unit,unit)) ),
inference(equality_proxy_replacement,[],[f233,f375]) ).
fof(f233,plain,
( e2 = op(unit,unit)
| ~ sP2 ),
inference(definition_unfolding,[],[f131,f148,f148]) ).
fof(f131,plain,
( op(e0,e0) = e2
| ~ sP2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f445,plain,
( ~ sP2
| sQ3_eqProxy(e2,op(e1,e1)) ),
inference(equality_proxy_replacement,[],[f130,f375]) ).
fof(f130,plain,
( ~ sP2
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f462,plain,
sQ3_eqProxy(unit,op(unit,unit)),
inference(equality_proxy_replacement,[],[f183,f375]) ).
fof(f183,plain,
unit = op(unit,unit),
inference(definition_unfolding,[],[f76,f148,f148]) ).
fof(f76,plain,
e0 = op(e0,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
( e0 = op(unit,e0)
& e1 = op(unit,e1)
& e2 = op(e2,unit)
& e0 = op(e0,unit)
& e1 = op(e1,unit)
& ( e3 = unit
| e2 = unit
| e1 = unit
| e0 = unit )
& e2 = op(unit,e2)
& e3 = op(unit,e3)
& e3 = op(e3,unit) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f495,plain,
( ~ sP1
| sQ3_eqProxy(op(e2,e2),unit) ),
inference(equality_proxy_replacement,[],[f235,f375]) ).
fof(f235,plain,
( op(e2,e2) = unit
| ~ sP1 ),
inference(definition_unfolding,[],[f134,f148]) ).
fof(f134,plain,
( e0 = op(e2,e2)
| ~ sP1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f430,plain,
( sP2
| sP0
| sQ3_eqProxy(e3,op(e3,e3))
| sP1 ),
inference(equality_proxy_replacement,[],[f143,f375]) ).
fof(f143,plain,
( sP1
| sP2
| e3 = op(e3,e3)
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f423,plain,
( sP0
| sQ3_eqProxy(e3,op(e2,e2))
| sP2
| sP1 ),
inference(equality_proxy_replacement,[],[f146,f375]) ).
fof(f146,plain,
( sP0
| sP2
| sP1
| e3 = op(e2,e2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f403,plain,
( sQ3_eqProxy(e2,op(e3,e3))
| ~ sP2 ),
inference(equality_proxy_replacement,[],[f129,f375]) ).
fof(f129,plain,
( e2 = op(e3,e3)
| ~ sP2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f447,plain,
( ~ sP0
| sQ3_eqProxy(e1,op(unit,unit)) ),
inference(equality_proxy_replacement,[],[f238,f375]) ).
fof(f238,plain,
( e1 = op(unit,unit)
| ~ sP0 ),
inference(definition_unfolding,[],[f138,f148,f148]) ).
fof(f138,plain,
( op(e0,e0) = e1
| ~ sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f397,plain,
( ~ sP0
| sQ3_eqProxy(e1,op(e3,e3)) ),
inference(equality_proxy_replacement,[],[f136,f375]) ).
fof(f136,plain,
( ~ sP0
| e1 = op(e3,e3) ),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ALG036+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n009.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 : Mon Aug 29 14:49:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.48 % (13756)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.18/0.48 % (13748)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.49 % (13758)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.18/0.49 % (13744)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.50 % (13748)First to succeed.
% 0.18/0.50 % (13750)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.50 % (13741)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.50 % (13745)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.50 % (13747)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.50 % (13741)Instruction limit reached!
% 0.18/0.50 % (13741)------------------------------
% 0.18/0.50 % (13741)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50 % (13741)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50 % (13741)Termination reason: Unknown
% 0.18/0.50 % (13741)Termination phase: Saturation
% 0.18/0.50
% 0.18/0.50 % (13741)Memory used [KB]: 5500
% 0.18/0.50 % (13741)Time elapsed: 0.005 s
% 0.18/0.50 % (13741)Instructions burned: 7 (million)
% 0.18/0.50 % (13741)------------------------------
% 0.18/0.50 % (13741)------------------------------
% 0.18/0.50 % (13735)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.51 % (13734)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.18/0.51 % (13744)Also succeeded, but the first one will report.
% 0.18/0.51 % (13748)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (13748)------------------------------
% 0.18/0.51 % (13748)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51 % (13748)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51 % (13748)Termination reason: Refutation
% 0.18/0.51
% 0.18/0.51 % (13748)Memory used [KB]: 5884
% 0.18/0.51 % (13748)Time elapsed: 0.013 s
% 0.18/0.51 % (13748)Instructions burned: 9 (million)
% 0.18/0.51 % (13748)------------------------------
% 0.18/0.51 % (13748)------------------------------
% 0.18/0.51 % (13733)Success in time 0.172 s
%------------------------------------------------------------------------------