%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG402-1 : 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 : n009.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 09:30:29 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.35s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 26 ( 16 unt; 0 def)
% Number of atoms : 38 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f85,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f88,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| X1 = c_HOL_Ozero__class_Ozero(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f89,plain,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(reorient_equations,[],[f88]) ).
fof(f182,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f354,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f361,axiom,
! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f521,axiom,
! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f535,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f536,plain,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) ),
inference(reorient_equations,[],[f535]) ).
fof(f1139,negated_conjecture,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1227,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(f1236,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1242,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1352,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(definition_unfolding,[],[f1139,f182,f182]) ).
fof(f1416,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0,
inference(resolution,[],[f354,f1242]) ).
fof(f1446,plain,
! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[],[f361,f1352]) ).
fof(f1455,plain,
! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[],[f1446,f1227]) ).
fof(f1457,plain,
! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1455,f521]) ).
fof(f1627,plain,
! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(resolution,[],[f536,f1242]) ).
fof(f1925,plain,
! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[],[f1457,f1627]) ).
fof(f1933,plain,
! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1925,f1416]) ).
fof(f1938,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(resolution,[],[f1933,f89]) ).
fof(f1939,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[],[f1938,f1227]) ).
fof(f1986,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
inference(superposition,[],[f85,f1939]) ).
fof(f1993,plain,
~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(trivial_inequality_removal,[],[f1986]) ).
fof(f2012,plain,
$false,
inference(forward_subsumption_resolution,[],[f1993,f1236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG402-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n009.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:18:45 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.35 % (3416204)Will run a generic schedule for satisfiability detection.
% 0.21/0.35 % (3416211)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2364437467:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.35 % (3416210)% WARNING: option uhcvi not known.
% 0.21/0.35 % (3416209)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2759490011_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.35 % (3416210)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2761117549:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.35 % (3416212)dis+10_1_sil=32000:sp=arity:random_seed=1412427823:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.35 % (3416213)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1694398667:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.35 % (3416214)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1460042518:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.35 % (3416215)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3723291286:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.35 % (3416212) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3416204-3416212"...
% 0.21/0.35 % (3416212)...printing done.
% 0.21/0.35 % (3416212)Refutation found. Thanks to Tanya!
% 0.21/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.35 % (3416212)------------------------------
% 0.21/0.35 % (3416212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (3416212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (3416212)CaDiCaL version: 2.1.3
% 0.21/0.35 % (3416212)Termination reason: Refutation
% 0.21/0.35 % (3416212)Time elapsed: 0.031 s
% 0.21/0.35 % (3416212)Peak memory usage: 13 MB
% 0.21/0.35 % (3416212)Instructions burned: 45 (million)
% 0.21/0.35 % (3416204)Success in time 0.106 s
% 0.21/0.35 % Vampire exiting
%------------------------------------------------------------------------------