%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM830^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:19:36 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 94 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 453 ( 9 ~; 0 |; 20 &; 398 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 8 con; 0-4 aty)
% ( 22 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 62 ( 28 ^; 34 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
n: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c0: n ).
thf(func_def_1,type,
cS: n > n ).
thf(func_def_2,type,
c_plus: n > n > n ).
thf(func_def_3,type,
c_star: n > n > n ).
thf(func_def_4,type,
cPA_1: $o ).
thf(func_def_5,type,
cPA_2: $o ).
thf(func_def_6,type,
cPA_3: $o ).
thf(func_def_7,type,
cPA_4: $o ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(f1,axiom,
( cPA_1
= ( ! [X0: n] :
( ( c_plus @ X0 @ c0 )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_1_def) ).
thf(f2,axiom,
( cPA_2
= ( ! [X0: n,X1: n] :
( ( c_plus @ X0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_2_def) ).
thf(f3,axiom,
( cPA_3
= ( ! [X0: n] :
( ( c_star @ X0 @ c0 )
= c0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_3_def) ).
thf(f4,axiom,
( cPA_4
= ( ! [X0: n,X1: n] :
( ( c_star @ X0 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ X0 @ X1 ) @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_4_def) ).
thf(f5,conjecture,
( ( cPA_4
& cPA_3
& cPA_2
& cPA_1 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_THM1) ).
thf(f6,negated_conjecture,
~ ( ( cPA_4
& cPA_3
& cPA_2
& cPA_1 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( cPA_1
= ( !! @ n
@ ^ [Y0: n] :
( ( c_plus @ Y0 @ c0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
( cPA_2
= ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_plus @ Y1 @ ( cS @ Y0 ) )
= ( cS @ ( c_plus @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f9,plain,
( cPA_3
= ( !! @ n
@ ^ [Y0: n] :
( c0
= ( c_star @ Y0 @ c0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f10,plain,
( cPA_4
= ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_star @ Y1 @ ( cS @ Y0 ) )
= ( c_plus @ ( c_star @ Y1 @ Y0 ) @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f11,plain,
~ ( ( cPA_4
& cPA_3
& cPA_2
& cPA_1 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
~ ( ( ( cPA_4 = $true )
& ( cPA_3 = $true )
& ( cPA_2 = $true )
& ( cPA_1 = $true ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) )
& ( cPA_4 = $true )
& ( cPA_3 = $true )
& ( cPA_2 = $true )
& ( cPA_1 = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) )
& ( cPA_4 = $true )
& ( cPA_3 = $true )
& ( cPA_2 = $true )
& ( cPA_1 = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( cPA_1
= ( !! @ n
@ ^ [Y0: n] :
( ( c_plus @ Y0 @ c0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,plain,
( cPA_2
= ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_plus @ Y1 @ ( cS @ Y0 ) )
= ( cS @ ( c_plus @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( cPA_3
= ( !! @ n
@ ^ [Y0: n] :
( c0
= ( c_star @ Y0 @ c0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
( cPA_4
= ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_star @ Y1 @ ( cS @ Y0 ) )
= ( c_plus @ ( c_star @ Y1 @ Y0 ) @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
cPA_1 = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
cPA_2 = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
cPA_3 = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
cPA_4 = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f26,plain,
( ( !! @ n
@ ^ [Y0: n] :
( ( c_plus @ Y0 @ c0 )
= Y0 ) )
= $true ),
inference(definition_unfolding,[],[f15,f19]) ).
thf(f27,plain,
( ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_plus @ Y1 @ ( cS @ Y0 ) )
= ( cS @ ( c_plus @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f16,f20]) ).
thf(f28,plain,
( ( !! @ n
@ ^ [Y0: n] :
( c0
= ( c_star @ Y0 @ c0 ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f21]) ).
thf(f29,plain,
( ( !! @ n
@ ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_star @ Y1 @ ( cS @ Y0 ) )
= ( c_plus @ ( c_star @ Y1 @ Y0 ) @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f22]) ).
thf(f30,plain,
! [X1: n] :
( $true
= ( ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_star @ Y1 @ ( cS @ Y0 ) )
= ( c_plus @ ( c_star @ Y1 @ Y0 ) @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: n] :
( $true
= ( !! @ n
@ ^ [Y0: n] :
( ( c_star @ Y0 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ Y0 @ X1 ) @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: n,X1: n] :
( $true
= ( ^ [Y0: n] :
( ( c_star @ Y0 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ Y0 @ X1 ) @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: n,X1: n] :
( $true
= ( ( c_star @ X2 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ X2 @ X1 ) @ X2 ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X2: n,X1: n] :
( ( c_star @ X2 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ X2 @ X1 ) @ X2 ) ),
inference(equality_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X1: n] :
( $true
= ( ^ [Y0: n] :
( c0
= ( c_star @ Y0 @ c0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f36,plain,
! [X1: n] :
( $true
= ( c0
= ( c_star @ X1 @ c0 ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X1: n] :
( c0
= ( c_star @ X1 @ c0 ) ),
inference(equality_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X1: n] :
( $true
= ( ^ [Y0: n] :
( !! @ n
@ ^ [Y1: n] :
( ( c_plus @ Y1 @ ( cS @ Y0 ) )
= ( cS @ ( c_plus @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f39,plain,
! [X1: n] :
( $true
= ( !! @ n
@ ^ [Y0: n] :
( ( c_plus @ Y0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: n,X1: n] :
( $true
= ( ^ [Y0: n] :
( ( c_plus @ Y0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: n,X1: n] :
( $true
= ( ( c_plus @ X2 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: n,X1: n] :
( ( c_plus @ X2 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X1: n] :
( $true
= ( ^ [Y0: n] :
( ( c_plus @ Y0 @ c0 )
= Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f44,plain,
! [X1: n] :
( $true
= ( ( c_plus @ X1 @ c0 )
= X1 ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ),
inference(equality_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X0: n] :
( ( c_star @ X0 @ ( cS @ c0 ) )
= ( c_plus @ c0 @ X0 ) ),
inference(constrained_superposition,[],[f34,f37]) ).
thf(f48,plain,
! [X0: n,X1: n] :
( ( cS @ ( c_plus @ ( c_star @ ( cS @ X0 ) @ X1 ) @ X0 ) )
= ( c_star @ ( cS @ X0 ) @ ( cS @ X1 ) ) ),
inference(constrained_superposition,[],[f34,f42]) ).
thf(f51,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) ) ),
inference(forward_demodulation,[],[f23,f42]) ).
thf(f52,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ c0 ) ) ) ),
inference(forward_demodulation,[],[f51,f42]) ).
thf(f53,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(forward_demodulation,[],[f52,f45]) ).
thf(f72,plain,
! [X0: n,X1: n] :
( ( c_star @ ( cS @ ( cS @ X0 ) ) @ ( cS @ X1 ) )
= ( cS @ ( cS @ ( c_plus @ ( c_star @ ( cS @ ( cS @ X0 ) ) @ X1 ) @ X0 ) ) ) ),
inference(constrained_superposition,[],[f48,f42]) ).
thf(f127,plain,
! [X0: n] :
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ X0 ) )
= ( cS @ ( cS @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ X0 ) ) ) ),
inference(constrained_superposition,[],[f72,f45]) ).
thf(f143,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( cS @ ( cS @ ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) ) ) ) ),
inference(constrained_superposition,[],[f127,f46]) ).
thf(f155,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( cS @ ( cS @ ( cS @ ( c_plus @ c0 @ ( cS @ c0 ) ) ) ) ) ),
inference(forward_demodulation,[],[f143,f42]) ).
thf(f157,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( cS @ ( cS @ ( cS @ ( cS @ ( c_plus @ c0 @ c0 ) ) ) ) ) ),
inference(forward_demodulation,[],[f155,f42]) ).
thf(f159,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(forward_demodulation,[],[f157,f45]) ).
thf(f161,plain,
$false,
inference(forward_subsumption_resolution,[],[f159,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM830^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:04:24 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.27 % (3115701)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (3115709)dis+10_1_sil=32000:sp=arity:random_seed=1199684457:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (3115707)% WARNING: option uhcvi not known.
% 0.19/0.27 % (3115709) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3115701-3115709"...
% 0.19/0.27 % (3115708)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2529336773:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (3115709)...printing done.
% 0.19/0.27 % (3115706)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1615825968_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (3115707)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2607598846:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (3115709)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (3115709)------------------------------
% 0.19/0.27 % (3115709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3115709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3115709)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3115709)Termination reason: Refutation
% 0.19/0.27 % (3115709)Time elapsed: 0.006 s
% 0.19/0.27 % (3115709)Peak memory usage: 12 MB
% 0.19/0.27 % (3115709)Instructions burned: 20 (million)
% 0.19/0.27 % (3115701)Success in time 0.035 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------