%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV626-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 : Tue Sep 29 01:26:09 PM UTC 2026
% Result : Unsatisfiable 1.09s 0.64s
% Output : Refutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 8 unt; 0 def)
% Number of atoms : 12 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f500,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1043,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
fof(f1044,plain,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) ),
inference(reorient_equations,[],[f1043]) ).
fof(f1115,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1219,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1260,plain,
! [X2,X0,X1] : c_Power_Opower__class_Opower(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
inference(resolution,[],[f1044,f1219]) ).
fof(f1267,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[],[f1115,f1260]) ).
fof(f1270,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1267,f1260]) ).
fof(f9840,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[],[f1270,f500]) ).
fof(f9848,plain,
$false,
inference(trivial_inequality_removal,[],[f9840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV626-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n003.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 12:06:27 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 1.09/0.64 % (1539496)Will run a generic schedule for satisfiability detection.
% 1.09/0.64 % (1539502)% WARNING: option uhcvi not known.
% 1.09/0.64 % (1539502)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2086855650:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.09/0.64 % (1539501)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=764267022_2999 on theBenchmark for (2999ds/0Mi)
% 1.09/0.64 % (1539505)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=311448375:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.09/0.64 % (1539503)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3342238425:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.09/0.64 % (1539504)dis+10_1_sil=32000:sp=arity:random_seed=739155974:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.09/0.64 % (1539506)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1494463910:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.09/0.64 % (1539507)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3749290665:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.09/0.64 % (1539504)Instruction limit reached!
% 1.09/0.64 % (1539504)------------------------------
% 1.09/0.64 % (1539504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.64 % (1539504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.64 % (1539504)CaDiCaL version: 2.1.3
% 1.09/0.64 % (1539504)Termination reason: Instruction limit
% 1.09/0.64 % (1539504)Termination phase: Saturation
% 1.09/0.64 % (1539504)Time elapsed: 0.068 s
% 1.09/0.64 % (1539504)Peak memory usage: 13 MB
% 1.09/0.64 % (1539504)Instructions burned: 104 (million)
% 1.09/0.64 % (1539505)Instruction limit reached!
% 1.09/0.64 % (1539505)------------------------------
% 1.09/0.64 % (1539505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.64 % (1539505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.64 % (1539505)CaDiCaL version: 2.1.3
% 1.09/0.64 % (1539505)Termination reason: Instruction limit
% 1.09/0.64 % (1539505)Termination phase: Saturation
% 1.09/0.64 % (1539505)Time elapsed: 0.074 s
% 1.09/0.64 % (1539505)Peak memory usage: 14 MB
% 1.09/0.64 % (1539505)Instructions burned: 121 (million)
% 1.09/0.64 % (1539515)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=726683039:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.09/0.64 % (1539506)Instruction limit reached!
% 1.09/0.64 % (1539506)------------------------------
% 1.09/0.64 % (1539506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.64 % (1539506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.64 % (1539506)CaDiCaL version: 2.1.3
% 1.09/0.64 % (1539506)Termination reason: Instruction limit
% 1.09/0.64 % (1539506)Termination phase: Saturation
% 1.09/0.64 % (1539506)Time elapsed: 0.091 s
% 1.09/0.64 % (1539506)Peak memory usage: 14 MB
% 1.09/0.64 % (1539506)Instructions burned: 132 (million)
% 1.09/0.64 % (1539516)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2521657507:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.09/0.64 % TRYING [1]
% 1.09/0.64 % (1539507)Instruction limit reached!
% 1.09/0.64 % (1539507)------------------------------
% 1.09/0.64 % (1539507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.64 % (1539507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.64 % (1539507)CaDiCaL version: 2.1.3
% 1.09/0.64 % (1539507)Termination reason: Instruction limit
% 1.09/0.64 % (1539507)Termination phase: Saturation
% 1.09/0.64 % (1539507)Time elapsed: 0.099 s
% 1.09/0.64 % (1539507)Peak memory usage: 14 MB
% 1.09/0.64 % (1539507)Instructions burned: 160 (million)
% 1.09/0.64 % TRYING [2]
% 1.09/0.64 % (1539518)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=2498805655:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.09/0.64 % (1539520)ott-21_1_sil=16000:fs=off:random_seed=3509572293:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.09/0.64 % (1539516)Instruction limit reached!
% 1.09/0.64 % (1539516)------------------------------
% 1.09/0.64 % (1539516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.64 % (1539516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.64 % (1539516)CaDiCaL version: 2.1.3
% 1.09/0.64 % (1539516)Termination reason: Instruction limit
% 1.09/0.64 % (1539516)Termination phase: Saturation
% 1.09/0.64 % (1539516)Time elapsed: 0.079 s
% 1.09/0.64 % (1539516)Peak memory usage: 14 MB
% 1.09/0.64 % (1539516)Instructions burned: 131 (million)
% 1.09/0.64 % TRYING [1]
% 1.09/0.64 % TRYING [3]
% 1.09/0.64 % TRYING [2]
% 1.09/0.64 % (1539523)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1288879384:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.09/0.64 % (1539520)Instruction limit reached!
% 1.09/0.64 % (1539520)------------------------------
% 1.09/0.64 % (1539520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.64 % (1539520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.64 % (1539520)CaDiCaL version: 2.1.3
% 1.09/0.64 % (1539520)Termination reason: Instruction limit
% 1.09/0.64 % (1539520)Termination phase: Saturation
% 1.09/0.64 % (1539520)Time elapsed: 0.080 s
% 1.09/0.64 % (1539520)Peak memory usage: 13 MB
% 1.09/0.64 % (1539520)Instructions burned: 181 (million)
% 1.09/0.64 % (1539525)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1449800588:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.09/0.64 % TRYING [3]
% 1.09/0.64 % TRYING [1]
% 1.09/0.64 % TRYING [2]
% 1.09/0.64 % (1539518) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1539496-1539518"...
% 1.09/0.64 % (1539518)...printing done.
% 1.09/0.64 % (1539518)Refutation found. Thanks to Tanya!
% 1.09/0.64 % SZS status Unsatisfiable for theBenchmark
% 1.09/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 1.09/0.64 % (1539518)------------------------------
% 1.09/0.64 % (1539518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.64 % (1539518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.64 % (1539518)CaDiCaL version: 2.1.3
% 1.09/0.64 % (1539518)Termination reason: Refutation
% 1.09/0.64 % (1539518)Time elapsed: 0.234 s
% 1.09/0.64 % (1539518)Peak memory usage: 17 MB
% 1.09/0.64 % (1539518)Instructions burned: 442 (million)
% 1.09/0.64 % (1539496)Success in time 0.421 s
% 1.09/0.64 % Vampire exiting
%------------------------------------------------------------------------------