%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM727^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:19:24 AM UTC 2026
% Result : Theorem 1.08s 0.47s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 40 unt; 0 typ; 6 def)
% Number of atoms : 50 ( 49 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 251 ( 12 ~; 4 |; 0 &; 234 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: frac ).
thf(func_def_1,type,
y: frac ).
thf(func_def_2,type,
z: frac ).
thf(func_def_3,type,
ts: nat > nat > nat ).
thf(func_def_4,type,
num: frac > nat ).
thf(func_def_5,type,
den: frac > nat ).
thf(func_def_7,type,
sF0: nat ).
thf(func_def_8,type,
sF1: nat ).
thf(func_def_9,type,
sF2: nat ).
thf(func_def_10,type,
sF3: nat ).
thf(func_def_11,type,
sF4: nat ).
thf(func_def_12,type,
sF5: nat ).
thf(f1,axiom,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(f2,axiom,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f) ).
thf(f3,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ts @ X0 @ X2 )
= ( ts @ X1 @ X2 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz33b) ).
thf(f4,axiom,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(f5,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( ts @ ( ts @ X0 @ X1 ) @ X2 )
= ( ts @ X0 @ ( ts @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz31) ).
thf(f6,conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(f7,negated_conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( X0 = X1 )
| ( ( ts @ X0 @ X2 )
!= ( ts @ X1 @ X2 ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f10,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f11,plain,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f12,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( ts @ X0 @ X2 )
!= ( ts @ X1 @ X2 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f14,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ ( ts @ X0 @ X1 ) @ X2 )
= ( ts @ X0 @ ( ts @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f15,plain,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,definition,
( sF0
= ( num @ x ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f17,plain,
( ( num @ x )
= sF0 ),
inference(reorient_equations,[],[f16]) ).
thf(f18,definition,
( sF1
= ( den @ z ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f19,plain,
( ( den @ z )
= sF1 ),
inference(reorient_equations,[],[f18]) ).
thf(f20,definition,
( sF2
= ( ts @ sF0 @ sF1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f21,plain,
( ( ts @ sF0 @ sF1 )
= sF2 ),
inference(reorient_equations,[],[f20]) ).
thf(f22,definition,
( sF3
= ( num @ z ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f23,plain,
( ( num @ z )
= sF3 ),
inference(reorient_equations,[],[f22]) ).
thf(f24,definition,
( sF4
= ( den @ x ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f25,plain,
( ( den @ x )
= sF4 ),
inference(reorient_equations,[],[f24]) ).
thf(f26,definition,
( sF5
= ( ts @ sF3 @ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f27,plain,
( ( ts @ sF3 @ sF4 )
= sF5 ),
inference(reorient_equations,[],[f26]) ).
thf(f28,plain,
sF2 != sF5,
inference(definition_folding,[],[f15,f27,f25,f23,f21,f19,f17]) ).
thf(f38,plain,
( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ sF0 @ ( den @ y ) ) ),
inference(constrained_superposition,[],[f10,f17]) ).
thf(f43,plain,
( ( ts @ sF0 @ ( den @ y ) )
= ( ts @ ( num @ y ) @ sF4 ) ),
inference(forward_demodulation,[],[f38,f25]) ).
thf(f46,plain,
( ( ts @ sF0 @ ( den @ y ) )
= ( ts @ sF4 @ ( num @ y ) ) ),
inference(forward_demodulation,[],[f43,f13]) ).
thf(f53,plain,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ sF3 @ ( den @ y ) ) ),
inference(constrained_superposition,[],[f11,f23]) ).
thf(f58,plain,
( ( ts @ sF3 @ ( den @ y ) )
= ( ts @ ( num @ y ) @ sF1 ) ),
inference(forward_demodulation,[],[f53,f19]) ).
thf(f61,plain,
( ( ts @ sF3 @ ( den @ y ) )
= ( ts @ sF1 @ ( num @ y ) ) ),
inference(forward_demodulation,[],[f58,f13]) ).
thf(f67,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ ( ts @ X0 @ X1 ) @ X2 )
= ( ts @ X1 @ ( ts @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f14,f13]) ).
thf(f71,plain,
! [X0: nat] :
( ( ts @ sF0 @ ( ts @ sF1 @ X0 ) )
= ( ts @ sF2 @ X0 ) ),
inference(constrained_superposition,[],[f14,f21]) ).
thf(f72,plain,
! [X0: nat] :
( ( ts @ sF3 @ ( ts @ sF4 @ X0 ) )
= ( ts @ sF5 @ X0 ) ),
inference(constrained_superposition,[],[f14,f27]) ).
thf(f140,plain,
! [X0: nat,X1: nat] :
( ( ( ts @ X1 @ X0 )
!= ( ts @ sF0 @ ( ts @ sF1 @ X0 ) ) )
| ( sF2 = X1 ) ),
inference(constrained_superposition,[],[f12,f71]) ).
thf(f268,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ X0 @ ( ts @ X1 @ X2 ) )
= ( ts @ X1 @ ( ts @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f14,f67]) ).
thf(f1096,plain,
! [X0: nat] :
( ( ( ts @ sF0 @ ( ts @ sF1 @ X0 ) )
!= ( ts @ sF3 @ ( ts @ sF4 @ X0 ) ) )
| ( sF2 = sF5 ) ),
inference(constrained_superposition,[],[f140,f72]) ).
thf(f1129,plain,
! [X0: nat] :
( ( ts @ sF0 @ ( ts @ sF1 @ X0 ) )
!= ( ts @ sF3 @ ( ts @ sF4 @ X0 ) ) ),
inference(forward_subsumption_resolution,[],[f1096,f28]) ).
thf(f1140,plain,
( ( ts @ sF0 @ ( ts @ sF1 @ ( num @ y ) ) )
!= ( ts @ sF3 @ ( ts @ sF0 @ ( den @ y ) ) ) ),
inference(constrained_superposition,[],[f1129,f46]) ).
thf(f1151,plain,
( ( ts @ sF0 @ ( ts @ sF3 @ ( den @ y ) ) )
!= ( ts @ sF0 @ ( ts @ sF1 @ ( num @ y ) ) ) ),
inference(forward_demodulation,[],[f1140,f268]) ).
thf(f1154,plain,
( ( ts @ sF0 @ ( ts @ sF1 @ ( num @ y ) ) )
!= ( ts @ sF0 @ ( ts @ sF1 @ ( num @ y ) ) ) ),
inference(forward_demodulation,[],[f1151,f61]) ).
thf(f1155,plain,
$false,
inference(trivial_inequality_removal,[],[f1154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM727^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:44:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/0.47 % (2050141)Will run a generic schedule for satisfiability detection.
% 1.08/0.47 % (2050148)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1825254123:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.08/0.47 % (2050147)% WARNING: option uhcvi not known.
% 1.08/0.47 % (2050147)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2148821140:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.08/0.47 % (2050146)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=151730913_2999 on theBenchmark for (2999ds/0Mi)
% 1.08/0.47 % (2050149)dis+10_1_sil=32000:sp=arity:random_seed=3948633558:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.08/0.47 % (2050147)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.47 % (2050150)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=702879809:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.08/0.47 % Exception at run slice level
% 1.08/0.47 User error: % (2050147)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.08/0.47 Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.47 % (2050150)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.47 % (2050152)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2434931166:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.08/0.47 % (2050151)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3593279778:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.08/0.47 % (2050158)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1796248700:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.08/0.47 % Exception at run slice level
% 1.08/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.47 % (2050162)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1613488757:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.08/0.47 % (2050149)Instruction limit reached!
% 1.08/0.47 % (2050149)------------------------------
% 1.08/0.47 % (2050149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.47 % (2050149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.47 % (2050149)CaDiCaL version: 2.1.3
% 1.08/0.47 % (2050149)Termination reason: Instruction limit
% 1.08/0.47 % (2050149)Termination phase: Saturation
% 1.08/0.47 % (2050149)Time elapsed: 0.046 s
% 1.08/0.47 % (2050149)Peak memory usage: 11 MB
% 1.08/0.47 % (2050149)Instructions burned: 104 (million)
% 1.08/0.47 % (2050150)Instruction limit reached!
% 1.08/0.47 % (2050150)------------------------------
% 1.08/0.47 % (2050150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.47 % (2050150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.47 % (2050150)CaDiCaL version: 2.1.3
% 1.08/0.47 % (2050150)Termination reason: Instruction limit
% 1.08/0.47 % (2050150)Termination phase: Saturation
% 1.08/0.47 % (2050150)Time elapsed: 0.054 s
% 1.08/0.47 % (2050150)Peak memory usage: 12 MB
% 1.08/0.47 % (2050150)Instructions burned: 117 (million)
% 1.08/0.47 % (2050164)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3699874550:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.08/0.47 % (2050164)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.47 % (2050164)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.08/0.47 % (2050165)ott-21_1_sil=16000:fs=off:random_seed=3114640371:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.08/0.47 % (2050152)Instruction limit reached!
% 1.08/0.47 % (2050152)------------------------------
% 1.08/0.47 % (2050152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.47 % (2050152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.47 % (2050152)CaDiCaL version: 2.1.3
% 1.08/0.47 % (2050152)Termination reason: Instruction limit
% 1.08/0.47 % (2050152)Termination phase: Saturation
% 1.08/0.47 % (2050152)Time elapsed: 0.075 s
% 1.08/0.47 % (2050152)Peak memory usage: 12 MB
% 1.08/0.47 % (2050152)Instructions burned: 161 (million)
% 1.08/0.47 % (2050162)Instruction limit reached!
% 1.08/0.47 % (2050162)------------------------------
% 1.08/0.47 % (2050162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.47 % (2050162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.47 % (2050162)CaDiCaL version: 2.1.3
% 1.08/0.47 % (2050162)Termination reason: Instruction limit
% 1.08/0.47 % (2050162)Termination phase: Saturation
% 1.08/0.47 % (2050162)Time elapsed: 0.064 s
% 1.08/0.47 % (2050162)Peak memory usage: 12 MB
% 1.08/0.47 % (2050162)Instructions burned: 133 (million)
% 1.08/0.47 % (2050168)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3921519327:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.08/0.47 % (2050151)Instruction limit reached!
% 1.08/0.47 % (2050151)------------------------------
% 1.08/0.47 % (2050151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.47 % (2050151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.47 % (2050151)CaDiCaL version: 2.1.3
% 1.08/0.47 % (2050151)Termination reason: Instruction limit
% 1.08/0.47 % (2050151)Termination phase: Saturation
% 1.08/0.47 % (2050151)Time elapsed: 0.108 s
% 1.08/0.47 % (2050151)Peak memory usage: 12 MB
% 1.08/0.47 % (2050151)Instructions burned: 132 (million)
% 1.08/0.47 % (2050169)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2030235957:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.08/0.47 % Exception at run slice level
% 1.08/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.47 % (2050165)Instruction limit reached!
% 1.08/0.47 % (2050165)------------------------------
% 1.08/0.47 % (2050165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.47 % (2050165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.47 % (2050165)CaDiCaL version: 2.1.3
% 1.08/0.47 % (2050165)Termination reason: Instruction limit
% 1.08/0.47 % (2050165)Termination phase: Saturation
% 1.08/0.47 % (2050165)Time elapsed: 0.068 s
% 1.08/0.47 % (2050165)Peak memory usage: 11 MB
% 1.08/0.47 % (2050165)Instructions burned: 183 (million)
% 1.08/0.47 % (2050172)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=236255208:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.08/0.47 % (2050173)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=937094596:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.08/0.47 % Exception at run slice level
% 1.08/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.47 % (2050174)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1523924934:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.08/0.47 % (2050174)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.47 % (2050177)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3213777790:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.08/0.47 % (2050177)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.47 % (2050172) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2050141-2050172"...
% 1.08/0.47 % (2050172)...printing done.
% 1.08/0.47 % (2050172)Refutation found. Thanks to Tanya!
% 1.08/0.47 % SZS status Theorem for theBenchmark
% 1.08/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 1.08/0.47 % (2050172)------------------------------
% 1.08/0.47 % (2050172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.47 % (2050172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.47 % (2050172)CaDiCaL version: 2.1.3
% 1.08/0.47 % (2050172)Termination reason: Refutation
% 1.08/0.47 % (2050172)Time elapsed: 0.064 s
% 1.08/0.47 % (2050172)Peak memory usage: 12 MB
% 1.08/0.47 % (2050172)Instructions burned: 112 (million)
% 1.08/0.47 % (2050141)Success in time 0.249 s
% 1.08/0.47 % Vampire exiting
%------------------------------------------------------------------------------