TSTP Solution File: ALG001^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG001^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 : Mon May 20 18:21:42 EDT 2024
% Result : Theorem 0.11s 0.33s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 36 ( 6 unt; 21 typ; 0 def)
% Number of atoms : 312 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 20 avg)
% Number of connectives : 33 ( 13 ~; 0 |; 15 &; 0 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 82 ( 81 >; 1 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 3 con; 0-6 aty)
% Number of variables : 99 ( 0 ^ 61 !; 32 ?; 99 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_6,type,
sK0: g > b ).
thf(func_def_7,type,
sK1: b > a ).
thf(func_def_8,type,
sK2: g > g > g ).
thf(func_def_9,type,
sK3: b > b > b ).
thf(func_def_10,type,
sK4: a > a > a ).
thf(func_def_11,type,
sK5: g ).
thf(func_def_12,type,
sK6: g ).
thf(func_def_13,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_14,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_15,type,
vAND: $o > $o > $o ).
thf(func_def_16,type,
vOR: $o > $o > $o ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[],[f46]) ).
thf(f46,plain,
vAPP(b,a,sK1,vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,sK5),sK6))) != vAPP(b,a,sK1,vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,sK5),sK6))),
inference(forward_demodulation,[],[f45,f12]) ).
thf(f12,plain,
! [X10: g,X9: g] : ( vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,X9),X10)) = vAPP(b,b,vAPP(b,sTfun(b,b),sK3,vAPP(g,b,sK0,X9)),vAPP(g,b,sK0,X10)) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
( ( vAPP(b,a,sK1,vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,sK5),sK6))) != vAPP(a,a,vAPP(a,sTfun(a,a),sK4,vAPP(b,a,sK1,vAPP(g,b,sK0,sK5))),vAPP(b,a,sK1,vAPP(g,b,sK0,sK6))) )
& ! [X7: b,X8: b] : ( vAPP(b,a,sK1,vAPP(b,b,vAPP(b,sTfun(b,b),sK3,X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK4,vAPP(b,a,sK1,X7)),vAPP(b,a,sK1,X8)) )
& ! [X9: g,X10: g] : ( vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,X9),X10)) = vAPP(b,b,vAPP(b,sTfun(b,b),sK3,vAPP(g,b,sK0,X9)),vAPP(g,b,sK0,X10)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: g > b,X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ? [X5: g,X6: g] : ( vAPP(b,a,X1,vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X5),X6))) != vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,vAPP(g,b,X0,X5))),vAPP(b,a,X1,vAPP(g,b,X0,X6))) )
& ! [X7: b,X8: b] : ( vAPP(b,a,X1,vAPP(b,b,vAPP(b,sTfun(b,b),X3,X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,X7)),vAPP(b,a,X1,X8)) )
& ! [X9: g,X10: g] : ( vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X9),X10)) = vAPP(b,b,vAPP(b,sTfun(b,b),X3,vAPP(g,b,X0,X9)),vAPP(g,b,X0,X10)) ) )
=> ( ? [X6: g,X5: g] : ( vAPP(b,a,sK1,vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,X5),X6))) != vAPP(a,a,vAPP(a,sTfun(a,a),sK4,vAPP(b,a,sK1,vAPP(g,b,sK0,X5))),vAPP(b,a,sK1,vAPP(g,b,sK0,X6))) )
& ! [X8: b,X7: b] : ( vAPP(b,a,sK1,vAPP(b,b,vAPP(b,sTfun(b,b),sK3,X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK4,vAPP(b,a,sK1,X7)),vAPP(b,a,sK1,X8)) )
& ! [X10: g,X9: g] : ( vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,X9),X10)) = vAPP(b,b,vAPP(b,sTfun(b,b),sK3,vAPP(g,b,sK0,X9)),vAPP(g,b,sK0,X10)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ? [X6: g,X5: g] : ( vAPP(b,a,sK1,vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,X5),X6))) != vAPP(a,a,vAPP(a,sTfun(a,a),sK4,vAPP(b,a,sK1,vAPP(g,b,sK0,X5))),vAPP(b,a,sK1,vAPP(g,b,sK0,X6))) )
=> ( vAPP(b,a,sK1,vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,sK5),sK6))) != vAPP(a,a,vAPP(a,sTfun(a,a),sK4,vAPP(b,a,sK1,vAPP(g,b,sK0,sK5))),vAPP(b,a,sK1,vAPP(g,b,sK0,sK6))) ) ),
introduced(choice_axiom,[]) ).
thf(f8,plain,
? [X0: g > b,X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ? [X5: g,X6: g] : ( vAPP(b,a,X1,vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X5),X6))) != vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,vAPP(g,b,X0,X5))),vAPP(b,a,X1,vAPP(g,b,X0,X6))) )
& ! [X7: b,X8: b] : ( vAPP(b,a,X1,vAPP(b,b,vAPP(b,sTfun(b,b),X3,X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,X7)),vAPP(b,a,X1,X8)) )
& ! [X9: g,X10: g] : ( vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X9),X10)) = vAPP(b,b,vAPP(b,sTfun(b,b),X3,vAPP(g,b,X0,X9)),vAPP(g,b,X0,X10)) ) ),
inference(rectify,[],[f7]) ).
thf(f7,plain,
? [X0: g > b,X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ? [X9: g,X10: g] : ( vAPP(b,a,X1,vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X9),X10))) != vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,vAPP(g,b,X0,X9))),vAPP(b,a,X1,vAPP(g,b,X0,X10))) )
& ! [X5: b,X6: b] : ( vAPP(b,a,X1,vAPP(b,b,vAPP(b,sTfun(b,b),X3,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,X5)),vAPP(b,a,X1,X6)) )
& ! [X7: g,X8: g] : ( vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X7),X8)) = vAPP(b,b,vAPP(b,sTfun(b,b),X3,vAPP(g,b,X0,X7)),vAPP(g,b,X0,X8)) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
? [X0: g > b,X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ? [X9: g,X10: g] : ( vAPP(b,a,X1,vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X9),X10))) != vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,vAPP(g,b,X0,X9))),vAPP(b,a,X1,vAPP(g,b,X0,X10))) )
& ! [X5: b,X6: b] : ( vAPP(b,a,X1,vAPP(b,b,vAPP(b,sTfun(b,b),X3,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,X5)),vAPP(b,a,X1,X6)) )
& ! [X7: g,X8: g] : ( vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X7),X8)) = vAPP(b,b,vAPP(b,sTfun(b,b),X3,vAPP(g,b,X0,X7)),vAPP(g,b,X0,X8)) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,plain,
~ ! [X0: g > b,X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ( ! [X5: b,X6: b] : ( vAPP(b,a,X1,vAPP(b,b,vAPP(b,sTfun(b,b),X3,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,X5)),vAPP(b,a,X1,X6)) )
& ! [X7: g,X8: g] : ( vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X7),X8)) = vAPP(b,b,vAPP(b,sTfun(b,b),X3,vAPP(g,b,X0,X7)),vAPP(g,b,X0,X8)) ) )
=> ! [X9: g,X10: g] : ( vAPP(b,a,X1,vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X9),X10))) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,vAPP(g,b,X0,X9))),vAPP(b,a,X1,vAPP(g,b,X0,X10))) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: g > b,X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ( ! [X5: b,X6: b] : ( vAPP(b,a,X1,vAPP(b,b,vAPP(b,sTfun(b,b),X3,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,X5)),vAPP(b,a,X1,X6)) )
& ! [X5: g,X6: g] : ( vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X5),X6)) = vAPP(b,b,vAPP(b,sTfun(b,b),X3,vAPP(g,b,X0,X5)),vAPP(g,b,X0,X6)) ) )
=> ! [X5: g,X6: g] : ( vAPP(b,a,X1,vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X5),X6))) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,vAPP(g,b,X0,X5))),vAPP(b,a,X1,vAPP(g,b,X0,X6))) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: g > b,X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ( ! [X5: b,X6: b] : ( vAPP(b,a,X1,vAPP(b,b,vAPP(b,sTfun(b,b),X3,X5),X6)) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,X5)),vAPP(b,a,X1,X6)) )
& ! [X5: g,X6: g] : ( vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X5),X6)) = vAPP(b,b,vAPP(b,sTfun(b,b),X3,vAPP(g,b,X0,X5)),vAPP(g,b,X0,X6)) ) )
=> ! [X5: g,X6: g] : ( vAPP(b,a,X1,vAPP(g,b,X0,vAPP(g,g,vAPP(g,sTfun(g,g),X2,X5),X6))) = vAPP(a,a,vAPP(a,sTfun(a,a),X4,vAPP(b,a,X1,vAPP(g,b,X0,X5))),vAPP(b,a,X1,vAPP(g,b,X0,X6))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM133_pme) ).
thf(f45,plain,
vAPP(b,a,sK1,vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,sK5),sK6))) != vAPP(b,a,sK1,vAPP(b,b,vAPP(b,sTfun(b,b),sK3,vAPP(g,b,sK0,sK5)),vAPP(g,b,sK0,sK6))),
inference(superposition,[],[f14,f13]) ).
thf(f13,plain,
! [X8: b,X7: b] : ( vAPP(b,a,sK1,vAPP(b,b,vAPP(b,sTfun(b,b),sK3,X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK4,vAPP(b,a,sK1,X7)),vAPP(b,a,sK1,X8)) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
vAPP(b,a,sK1,vAPP(g,b,sK0,vAPP(g,g,vAPP(g,sTfun(g,g),sK2,sK5),sK6))) != vAPP(a,a,vAPP(a,sTfun(a,a),sK4,vAPP(b,a,sK1,vAPP(g,b,sK0,sK5))),vAPP(b,a,sK1,vAPP(g,b,sK0,sK6))),
inference(cnf_transformation,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : ALG001^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat May 18 23:24:37 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.31 % (19191)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (19192)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33 % Exception at run slice level
% 0.11/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.33 % (19198)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)
% 0.11/0.33 % (19194)WARNING: value z3 for option sas not known
% 0.11/0.33 % (19198)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.33 % (19195)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.33 % (19194)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)
% 0.11/0.33 % (19196)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)
% 0.11/0.33 % (19197)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)
% 0.11/0.33 % Exception at run slice level
% 0.11/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.33 % (19198)First to succeed.
% 0.11/0.33 % (19193)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.33 % Exception at run slice level
% 0.11/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.33 % (19198)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19191"
% 0.11/0.33 % (19196)Also succeeded, but the first one will report.
% 0.11/0.33 % (19197)Also succeeded, but the first one will report.
% 0.11/0.33 % (19198)Refutation found. Thanks to Tanya!
% 0.11/0.33 % SZS status Theorem for theBenchmark
% 0.11/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.33 % (19198)------------------------------
% 0.11/0.33 % (19198)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.33 % (19198)Termination reason: Refutation
% 0.11/0.33
% 0.11/0.33 % (19198)Memory used [KB]: 775
% 0.11/0.33 % (19198)Time elapsed: 0.005 s
% 0.11/0.33 % (19198)Instructions burned: 7 (million)
% 0.11/0.33 % (19191)Success in time 0.014 s
%------------------------------------------------------------------------------