%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG438-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:20:01 AM UTC 2026
% Result : Unsatisfiable 3.89s 1.34s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 5 unt; 0 def)
% Number of atoms : 7 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f299,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X1,X2,X0),X3,tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X3,X0),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pCons__left_0) ).
fof(f413,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f424,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f560,plain,
! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[],[f299,f424]) ).
fof(f1521,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[],[f413,f560]) ).
fof(f1524,plain,
$false,
inference(trivial_inequality_removal,[],[f1521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG438-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n001.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 20:30:19 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.89/1.34 % (683325)Input is clausal, will run a generic CNF schedule.
% 3.89/1.34 % (683332)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3845528121:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.89/1.34 % (683335)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=475917847:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.89/1.34 % (683333)lrs+10_1_sil=8000:sp=occurrence:random_seed=2393961017:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.89/1.34 % (683330)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2660993225:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.89/1.34 % (683331)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2539449297:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.89/1.34 % (683334)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1888172355:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.89/1.34 % (683336)dis-21_1_sil=8000:lcm=predicate:random_seed=1341436403:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.89/1.34 % (683335)First to succeed.
% 3.89/1.34 % (683335)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-683325"
% 3.89/1.34 % (683336)Also succeeded, but the first one will report.
% 3.89/1.34 % (683333)Instruction limit reached!
% 3.89/1.34 % (683333)------------------------------
% 3.89/1.34 % (683333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.34 % (683333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.34 % (683333)CaDiCaL version: 2.1.3
% 3.89/1.34 % (683333)Termination reason: Instruction limit
% 3.89/1.34 % (683333)Termination phase: Saturation
% 3.89/1.34 % (683333)Time elapsed: 0.060 s
% 3.89/1.34 % (683333)Peak memory usage: 89 MB
% 3.89/1.34 % (683333)Instructions burned: 108 (million)
% 3.89/1.34 % (683334)Instruction limit reached!
% 3.89/1.34 % (683334)------------------------------
% 3.89/1.34 % (683334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.34 % (683334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.34 % (683334)CaDiCaL version: 2.1.3
% 3.89/1.34 % (683334)Termination reason: Instruction limit
% 3.89/1.34 % (683334)Termination phase: Saturation
% 3.89/1.34 % (683334)Time elapsed: 0.060 s
% 3.89/1.34 % (683334)Peak memory usage: 88 MB
% 3.89/1.34 % (683334)Instructions burned: 114 (million)
% 3.89/1.34 % (683344)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2617698727:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.89/1.34 % (683344)Also succeeded, but the first one will report.
% 3.89/1.34 % (683345)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3530362846:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.89/1.34 % (683345)Also succeeded, but the first one will report.
% 3.89/1.34 % (683335)Refutation found. Thanks to Tanya!
% 3.89/1.34 % SZS status Unsatisfiable for theBenchmark
% 3.89/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.34 % (683335)------------------------------
% 3.89/1.34 % (683335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.34 % (683335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.34 % (683335)CaDiCaL version: 2.1.3
% 3.89/1.34 % (683335)Termination reason: Refutation
% 3.89/1.34 % (683335)Time elapsed: 0.050 s
% 3.89/1.34 % (683335)Peak memory usage: 90 MB
% 3.89/1.34 % (683335)Instructions burned: 75 (million)
% 3.89/1.34 % (683335)------------------------------
% 3.89/1.34 % (683335)------------------------------
% 3.89/1.34 % (683325)Success in time 0.468 s
% 3.89/1.34 % Vampire exiting
%------------------------------------------------------------------------------