TSTP Solution File: SEV116^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV116^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n021.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 16:01:52 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 229 ( 22 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 366 ( 6 ~; 0 |; 41 &; 253 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 131 ( 131 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 5 con; 0-3 aty)
% ( 25 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 65 ( 61 ^ 4 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: ( $i > $i > $o ) > $o ).
thf(func_def_3,type,
cSTRANGE_HO_ABBR: ( ( $i > $i > $o ) > $o ) > $i > $i > $o ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: $i > $i > $o ).
thf(f54,plain,
$false,
inference(trivial_inequality_removal,[],[f53]) ).
thf(f53,plain,
$false = $true,
inference(forward_demodulation,[],[f52,f16]) ).
thf(f16,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ y @ x ) )
=> ( Y0 @ x @ y ) ) ) ),
inference(binary_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( ( ( cS
@ ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( cS @ Y2 )
& ( Y2 @ Y0 @ Y1 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ x @ y ) )
=> ( Y0 @ y @ x ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ y @ x ) )
=> ( Y0 @ x @ y ) ) ) ) ),
inference(not_proxy_clausification,[],[f12]) ).
thf(f12,plain,
( ( ~ ( ( ( cS
@ ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( cS @ Y2 )
& ( Y2 @ Y0 @ Y1 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ x @ y ) )
=> ( Y0 @ y @ x ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ y @ x ) )
=> ( Y0 @ x @ y ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f11]) ).
thf(f11,plain,
( ( ~ ( ( ( cS
@ ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( Y0 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
@ cS ) )
& ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( Y0 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
@ cS
@ x
@ y ) )
=> ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( Y0 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
@ cS
@ y
@ x ) ) )
= $true ),
inference(definition_unfolding,[],[f9,f10,f10,f10]) ).
thf(f10,plain,
( cSTRANGE_HO_ABBR
= ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( Y0 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f6,plain,
( cSTRANGE_HO_ABBR
= ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( Y0 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
( cSTRANGE_HO_ABBR
= ( ^ [X0: ( $i > $i > $o ) > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( X3 @ X1 @ X2 )
& ( X0 @ X3 ) )
=> ( X3 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( cSTRANGE_HO_ABBR
= ( ^ [X0: ( $i > $i > $o ) > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( X3 @ X1 @ X2 )
& ( X0 @ X3 ) )
=> ( X3 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSTRANGE_HO_ABBR_def) ).
thf(f9,plain,
( ( ~ ( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
& ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ) )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f8,plain,
( ( ~ ( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
& ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ) )
= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
~ ( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
& ( cS @ ( cSTRANGE_HO_ABBR @ cS ) ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
inference(rectify,[],[f3]) ).
thf(f3,negated_conjecture,
~ ( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
& ( cS @ ( cSTRANGE_HO_ABBR @ cS ) ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
inference(negated_conjecture,[],[f2]) ).
thf(f2,conjecture,
( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
& ( cS @ ( cSTRANGE_HO_ABBR @ cS ) ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSTRANGE_HO_EXAMPLE) ).
thf(f52,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ y @ x ) )
=> ( Y0 @ x @ y ) ) ) ),
inference(boolean_simplification,[],[f51]) ).
thf(f51,plain,
( ( $true
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ y @ x ) )
=> ( Y0 @ x @ y ) ) ) )
= $true ),
inference(forward_demodulation,[],[f47,f32]) ).
thf(f32,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ x @ y ) )
=> ( Y0 @ y @ x ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( cS
@ ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( cS @ Y2 )
& ( Y2 @ Y0 @ Y1 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ x @ y ) )
=> ( Y0 @ y @ x ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f13]) ).
thf(f47,plain,
( $true
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ x @ y ) )
=> ( Y0 @ y @ x ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ y @ x ) )
=> ( Y0 @ x @ y ) ) ) ) ),
inference(boolean_simplification,[],[f46]) ).
thf(f46,plain,
( $true
= ( ( $true
& ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ x @ y ) )
=> ( Y0 @ y @ x ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ y @ x ) )
=> ( Y0 @ x @ y ) ) ) ) ),
inference(beta_eta_normalization,[],[f41]) ).
thf(f41,plain,
( $true
= ( ( $true
& ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( cS @ Y2 )
& ( Y2 @ Y0 @ Y1 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
@ x
@ y ) )
=> ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( cS @ Y2 )
& ( Y2 @ Y0 @ Y1 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
@ y
@ x ) ) ),
inference(superposition,[],[f37,f35]) ).
thf(f35,plain,
( ( cS
@ ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( cS @ Y2 )
& ( Y2 @ Y0 @ Y1 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f34]) ).
thf(f34,plain,
( ( ( cS
@ ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( cS @ Y2 )
& ( Y2 @ Y0 @ Y1 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[],[f17,f32]) ).
thf(f37,plain,
! [X1: $i > $i > $o] :
( $true
= ( ( ( cS @ X1 )
& ( X1 @ x @ y ) )
=> ( X1 @ y @ x ) ) ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( ( ( cS @ Y0 )
& ( Y0 @ x @ y ) )
=> ( Y0 @ y @ x ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SEV116^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.14/0.14 % Command : run_vampire %s %d THM
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 21 19:12:09 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running higher-order theorem proving
% 0.14/0.36 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.22/0.37 % (10839)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.38 % (10841)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)
% 0.22/0.38 % (10843)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)
% 0.22/0.38 % (10844)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)
% 0.22/0.38 % (10842)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (10840)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)
% 0.22/0.38 % (10845)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38 % (10842)Instruction limit reached!
% 0.22/0.38 % (10842)------------------------------
% 0.22/0.38 % (10842)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (10842)Termination reason: Unknown
% 0.22/0.38 % (10842)Termination phase: Saturation
% 0.22/0.38 % (10844)Refutation not found, incomplete strategy
% 0.22/0.38 % (10844)------------------------------
% 0.22/0.38 % (10844)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (10844)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.38
% 0.22/0.38
% 0.22/0.38 % (10844)Memory used [KB]: 5500
% 0.22/0.38 % (10844)Time elapsed: 0.003 s
% 0.22/0.38 % (10844)Instructions burned: 1 (million)
% 0.22/0.38 % (10844)------------------------------
% 0.22/0.38 % (10844)------------------------------
% 0.22/0.38 % (10843)Instruction limit reached!
% 0.22/0.38 % (10843)------------------------------
% 0.22/0.38 % (10843)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (10843)Termination reason: Unknown
% 0.22/0.38 % (10843)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (10843)Memory used [KB]: 5500
% 0.22/0.38 % (10843)Time elapsed: 0.003 s
% 0.22/0.38 % (10843)Instructions burned: 2 (million)
% 0.22/0.38 % (10843)------------------------------
% 0.22/0.38 % (10843)------------------------------
% 0.22/0.38
% 0.22/0.38 % (10842)Memory used [KB]: 5500
% 0.22/0.38 % (10842)Time elapsed: 0.003 s
% 0.22/0.38 % (10842)Instructions burned: 2 (million)
% 0.22/0.38 % (10842)------------------------------
% 0.22/0.38 % (10842)------------------------------
% 0.22/0.38 % (10841)Refutation not found, incomplete strategy
% 0.22/0.38 % (10841)------------------------------
% 0.22/0.38 % (10841)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (10841)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.38
% 0.22/0.38
% 0.22/0.38 % (10841)Memory used [KB]: 5500
% 0.22/0.38 % (10841)Time elapsed: 0.004 s
% 0.22/0.38 % (10841)Instructions burned: 3 (million)
% 0.22/0.38 % (10841)------------------------------
% 0.22/0.38 % (10841)------------------------------
% 0.22/0.38 % (10840)Instruction limit reached!
% 0.22/0.38 % (10840)------------------------------
% 0.22/0.38 % (10840)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (10840)Termination reason: Unknown
% 0.22/0.38 % (10840)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (10840)Memory used [KB]: 5500
% 0.22/0.38 % (10840)Time elapsed: 0.004 s
% 0.22/0.38 % (10840)Instructions burned: 5 (million)
% 0.22/0.38 % (10840)------------------------------
% 0.22/0.38 % (10840)------------------------------
% 0.22/0.39 % (10845)Instruction limit reached!
% 0.22/0.39 % (10845)------------------------------
% 0.22/0.39 % (10845)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (10845)Termination reason: Unknown
% 0.22/0.39 % (10845)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (10845)Memory used [KB]: 5628
% 0.22/0.39 % (10845)Time elapsed: 0.012 s
% 0.22/0.39 % (10845)Instructions burned: 18 (million)
% 0.22/0.39 % (10845)------------------------------
% 0.22/0.39 % (10845)------------------------------
% 0.22/0.39 % (10850)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.22/0.39 % (10848)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.22/0.39 % (10847)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.22/0.39 % (10850)First to succeed.
% 0.22/0.40 % (10846)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40 % (10849)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40 % (10850)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (10850)------------------------------
% 0.22/0.40 % (10850)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (10850)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (10850)Memory used [KB]: 5500
% 0.22/0.40 % (10850)Time elapsed: 0.006 s
% 0.22/0.40 % (10850)Instructions burned: 7 (million)
% 0.22/0.40 % (10850)------------------------------
% 0.22/0.40 % (10850)------------------------------
% 0.22/0.40 % (10838)Success in time 0.026 s
%------------------------------------------------------------------------------