TSTP Solution File: SEV059^5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV059^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n017.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 Jun 24 16:01:39 EDT 2024
% Result : Theorem 0.13s 0.39s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 167 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 312 ( 31 ~; 14 |; 27 &; 229 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 11 ^ 47 !; 4 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cG: b > b ).
thf(func_def_3,type,
cA: b > a ).
thf(func_def_4,type,
c_less_: a > a > $o ).
thf(func_def_5,type,
cF: b > b ).
thf(func_def_11,type,
sK0: b ).
thf(f24,plain,
$false,
inference(subsumption_resolution,[],[f22,f12]) ).
thf(f12,plain,
! [X4: b] :
( $true
= ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cF @ X4 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
( ( $true
!= ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) ) )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X1: a,X2: a,X3: a] :
( ( $true
!= ( c_less_ @ X3 @ X1 ) )
| ( $true
!= ( c_less_ @ X2 @ X3 ) )
| ( ( c_less_ @ X2 @ X1 )
= $true ) )
& ! [X4: b] :
( $true
= ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cF @ X4 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: b] :
( $true
!= ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cG @ X0 ) ) ) )
=> ( $true
!= ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
( ? [X0: b] :
( $true
!= ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cG @ X0 ) ) ) )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X1: a,X2: a,X3: a] :
( ( $true
!= ( c_less_ @ X3 @ X1 ) )
| ( $true
!= ( c_less_ @ X2 @ X3 ) )
| ( ( c_less_ @ X2 @ X1 )
= $true ) )
& ! [X4: b] :
( $true
= ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cF @ X4 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
( ? [X4: b] :
( $true
!= ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) ) )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X1: a,X2: a,X3: a] :
( ( $true
!= ( c_less_ @ X3 @ X1 ) )
| ( $true
!= ( c_less_ @ X2 @ X3 ) )
| ( ( c_less_ @ X2 @ X1 )
= $true ) )
& ! [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ? [X4: b] :
( $true
!= ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) ) )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X1: a,X2: a,X3: a] :
( ( ( c_less_ @ X2 @ X1 )
= $true )
| ( $true
!= ( c_less_ @ X2 @ X3 ) )
| ( $true
!= ( c_less_ @ X3 @ X1 ) ) )
& ! [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ( ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X1: a,X2: a,X3: a] :
( ( ( $true
= ( c_less_ @ X2 @ X3 ) )
& ( $true
= ( c_less_ @ X3 @ X1 ) ) )
=> ( ( c_less_ @ X2 @ X1 )
= $true ) )
& ! [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true ) )
=> ! [X4: b] :
( $true
= ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( $true
= ( c_less_ @ X4 @ X2 ) )
& ( $true
= ( c_less_ @ X3 @ X4 ) ) )
=> ( ( c_less_ @ X3 @ X2 )
= $true ) ) )
=> ! [X5: b] :
( ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) )
= $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: b] : ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
& ( cG
= ( ^ [X1: b] : ( cF @ ( cF @ X1 ) ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( c_less_ @ X4 @ X2 )
& ( c_less_ @ X3 @ X4 ) )
=> ( c_less_ @ X3 @ X2 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: b] : ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
& ( cG
= ( ^ [X4: b] : ( cF @ ( cF @ X4 ) ) ) )
& ! [X2: a,X0: a,X1: a] :
( ( ( c_less_ @ X1 @ X2 )
& ( c_less_ @ X0 @ X1 ) )
=> ( c_less_ @ X0 @ X2 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: b] : ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
& ( cG
= ( ^ [X4: b] : ( cF @ ( cF @ X4 ) ) ) )
& ! [X2: a,X0: a,X1: a] :
( ( ( c_less_ @ X1 @ X2 )
& ( c_less_ @ X0 @ X1 ) )
=> ( c_less_ @ X0 @ X2 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM89A_pme) ).
thf(f22,plain,
( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cF @ sK0 ) ) )
!= $true ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f20,plain,
( ( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cF @ sK0 ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f19,f12]) ).
thf(f19,plain,
! [X0: a] :
( ( $true
!= ( c_less_ @ X0 @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) ) )
| ( ( c_less_ @ ( cA @ sK0 ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f18]) ).
thf(f18,plain,
! [X0: a] :
( ( $true
!= ( c_less_ @ X0 @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) ) )
| ( $true != $true )
| ( ( c_less_ @ ( cA @ sK0 ) @ X0 )
!= $true ) ),
inference(superposition,[],[f17,f13]) ).
thf(f13,plain,
! [X2: a,X3: a,X1: a] :
( ( ( c_less_ @ X2 @ X1 )
= $true )
| ( $true
!= ( c_less_ @ X2 @ X3 ) )
| ( $true
!= ( c_less_ @ X3 @ X1 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( $true
!= ( c_less_ @ ( cA @ sK0 )
@ ( cA
@ ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) )
@ sK0 ) ) ) ),
inference(definition_unfolding,[],[f15,f14]) ).
thf(f14,plain,
( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( $true
!= ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV059^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.13 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n017.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 : Fri Jun 21 19:19:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 This is a TH0_THM_EQU_NAR problem
% 0.13/0.36 Running higher-order theorem proving
% 0.13/0.36 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.13/0.39 % (15253)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.39 % (15254)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.13/0.39 % (15255)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.13/0.39 % (15256)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.39 % (15257)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.39 % (15258)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.13/0.39 % (15259)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.39 % (15256)Instruction limit reached!
% 0.13/0.39 % (15256)------------------------------
% 0.13/0.39 % (15256)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (15256)Termination reason: Unknown
% 0.13/0.39 % (15256)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (15256)Memory used [KB]: 5373
% 0.13/0.39 % (15256)Time elapsed: 0.004 s
% 0.13/0.39 % (15256)Instructions burned: 2 (million)
% 0.13/0.39 % (15256)------------------------------
% 0.13/0.39 % (15256)------------------------------
% 0.13/0.39 % (15257)Instruction limit reached!
% 0.13/0.39 % (15257)------------------------------
% 0.13/0.39 % (15257)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (15257)Termination reason: Unknown
% 0.13/0.39 % (15257)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (15257)Memory used [KB]: 5500
% 0.13/0.39 % (15257)Time elapsed: 0.004 s
% 0.13/0.39 % (15257)Instructions burned: 2 (million)
% 0.13/0.39 % (15257)------------------------------
% 0.13/0.39 % (15257)------------------------------
% 0.13/0.39 % (15253)First to succeed.
% 0.13/0.39 % (15254)Instruction limit reached!
% 0.13/0.39 % (15254)------------------------------
% 0.13/0.39 % (15254)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (15254)Termination reason: Unknown
% 0.13/0.39 % (15254)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (15254)Memory used [KB]: 5500
% 0.13/0.39 % (15254)Time elapsed: 0.005 s
% 0.13/0.39 % (15254)Instructions burned: 4 (million)
% 0.13/0.39 % (15254)------------------------------
% 0.13/0.39 % (15254)------------------------------
% 0.13/0.39 % (15255)Also succeeded, but the first one will report.
% 0.13/0.39 % (15253)Refutation found. Thanks to Tanya!
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39 % (15253)------------------------------
% 0.13/0.39 % (15253)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (15253)Termination reason: Refutation
% 0.13/0.39
% 0.13/0.39 % (15253)Memory used [KB]: 5500
% 0.13/0.39 % (15253)Time elapsed: 0.005 s
% 0.13/0.39 % (15253)Instructions burned: 2 (million)
% 0.13/0.39 % (15253)------------------------------
% 0.13/0.39 % (15253)------------------------------
% 0.13/0.39 % (15252)Success in time 0.02 s
%------------------------------------------------------------------------------